PHILOSOPHY  AND  THE 
NEW  PHYSICS 


ROUG1ER 


PHILOSOPHY  AND  THE 
NEW  PHYSICS 


An  Essay  on  the  Relativity  Theory  and 
the  Theory  of  Quanta 


BY 

LOUIS  ROUGIER 

PROFESSEUR  AGREGE   DE  PHILOSOPHIE,   DOCTEUR  ES  LETTRES 

Authorized  Translation 

From  the  Author's  Corrected  Text  of 

'La  Materialisation  de  I'finergie" 

BY 
MORTON  MASIUS,  M.A.,  PH.D. 

PROFESSOR  OF  PHYSICS  IN  THE  WORCESTER  POLYTECHNIC  INSTITUTE 
TRANSLATOR  OF  M.   PLANCK'S  THEORY  OF   RADIATION 


PHILADELPHIA 

P.    BLAKISTON'S  SON   &  CO. 

1012  WALNUT   STREET 


COPYRIGHT,  1921,  BY  P.  BLAKISTON'S  SON  &  Co. 


THE  MAPLE  PRESS  YORK  PA 


TRANSLATOR'S  PREFACE 

The  recent  remarkable  developments  of  physical 
theories,  especially  those  concerned  with  relativity 
and  quanta  of  energy,  cannot  fail  to  have  far-reach- 
ing influences  on  philosophical  thought.  Physicists, 
as  a  rule,  are  too  much  occupied  with  their  special 
field  to  give  much  attention  to  matters  of  more 
general  philosophical  interest,  and  few  philosophers 
possess  the  knowledge  of  science  required  for  dis- 
cussing and  criticizing  fruitfully  the  work  of  the 
physicist.  Professor  Rougier's  very  wide  reading 
in  mathematical  and  experimental  Physics  has  en- 
abled him  to  present  and  interpret  the  new  ad- 
vances in  Physics  in  a  way  which  should  prove  of 
great  interest  to  both  philosopher  and  physicist. 
This  book  seems  to  mark  a  measurable  advance 
toward  a  confluence  of  the  broad  streams  of  philo- 
sophical and  scientific  enquiry. 

M.  M. 


449830 


CONTENTS 

CHAPTER  PAGE 

I.  THE  DUALISM  OF  MATTER  AND  ENERGY. 

1.  Introduction 1 

2.  The  Dualistic  Theory 3 

3.  The    Difficulties    of    the    Dualistic    Theory    and    the 

Check  given  to  the  Monistic  Attempts  at  Reduction       6 

4.  Ostwald's  Energetics 12 

5.  The   Insufficiency   of    Ostwald's    Energetics   and   the 

Experimental  Discovery  of  the  Inertia  of  Energy      .      15 

II.  MASS   AND   THE    RELATIVITY   PRINCIPLE. 

6.  The  Idea  of  Mass;  Einstein's  Equivalence  Principle 

and  Newton's  Principle  of  Action  and  Reaction    .    .     22 

7.  The  Relativity  Principle 28 

III.  ELECTROMAGNETIC  DYNAMICS. 

8.  The  Localization  of  Energy  Outside  of  Matter   ....     41 

9.  Electromagnetic    Inertia    and    the     Dynamics    of    an 

Electrified  Particle  in  Motion 47 

IV.  THE  ELECTRONIC  THEORY  OF  MATTER. 

10.  Lorentz's  Synthesis .'....     57 

11.  The  Dematerialization  of  Matter 62 

V.  THE  INERTIA  OF  ENERGY. 

12.  The  Materialization  of  Energy 73 

13.  The  Evaluation  of  the  Internal  Energy  of  Bodies  and 

the  Variations  of  Mass 84 

VI.  THE  WEIGHT  OF  ENERGY. 

14.  The  Weight  of  Energy;  Its  Experimental  Verifications.      91 

15.  The  Generalized  Principle  of  Relativity  and  Einstein's 

Theory  of  Gravitation 96 

16.  Astronomical  Verification 106 

vii 


Vlll  CONTENTS 

CHAPTER  PAGE 

VII.  THE  STRUCTURE  OF  ENERGY. 

17.  The  Success  of  the  Electronic  Theory;  the  Explanation 

of  the  Relations  of  Matter  and  Radiation 1 10 

18.  Check  to  the  Electronic  Theory;  Black  Radiation  and 

the  Quantum  Theory 120 

19.  The  Structure  of  Radiation 134 

20.  The  Physics  of  the  Discontinuous 143 

VIII.  CONCLUSION. 

21.  Conclusion 148 

BIBLIOGRAPHY 153 

INDEX  OF  NAMES.  157 


INTRODUCTION 

It  has  been  customary  since  the  time  of  Auguste 
Comte  (1795-1857)  to  distinguish  two  entirely 
separate  categories  of  problems:  those  which  may 
be  treated  by  the  methods  of  science  and  which 
are,  because  of  the  perfection  these  methods  have 
reached,  capable  of  being  solved  sooner  or  later,  and 
those  which,  being  beyond  these  methods,  lie  out- 
side of  the  limits  of  experience  and  on  that  account 
are  called  metaphysical  problems.  The  former 
problems,  taken  together,  mark  off  the  field  of  the 
exact  science;  the  latter  comprise  what  Herbert 
Spencer  and  Du  Bois-Reymond  have  called  the 
unknowable. 

We  have  no  criterion  by  means  of  which  to 
decide  a  priori  to  which  of  these  two  categories  a 
given  problem  belongs.  In  every  case  in  which  a 
philosophical  system  has  claimed  to  lay  down, 
dogmatically,  the  limits  to  our  experience,  later 
scientific  discoveries  have  seemed  to  make  a  point 
of  proving  it  to  be  wrong.  For  example,  the  real 
nature  of  phenomena,  according  to  Auguste  Comte, 
the  founder  of  positivism,  will  never  be  disclosed; 
"When  a  scientific  theory,"  declares  Poincare,1 

1  H.  Poincare,  La  valeur  de  la  Science,  p.  267. 

ix 


X  INTRODUCTION 

"claims  to  tell  us  what  heat,  what  electricity,  or  what 
life  really  is,  it  stands  convicted  at  the  outset.7' 
This  idea  led  Ostwald  to  his  Energetics,  and  Duhem 
to  his  Theory  of  Physics.  Who  at  the  present  time 
would  bind  himself  to  this  prudent  agnosticism,  to 
the  extent  of  doubting  the  objective  existence  of 
discontinuous  elements,  like  molecules,  atoms,  or 
electrons?  "The  atoms  are  no  longer  a  convenient 
fiction;  it  seems  to  us  that  we  can,  so  to  speak,  see 
them,  since  we  know  how  to  count  them/'1  as  Poin- 
care  had  to  admit  in  the  later  part  of  his  life  when 
confronted  by  the  achievements  of  the  atomic 
hypotheses. 

It  occurs  much  more  often  that  metaphysical 
problems,  supposedly  incapable  of  solution,  vanish, 
simply  because  the  progress  of  ideas  shows  that 
they  are  fictitious  problems  or  pseudo-problems, 
or  problems  which  have  been  badly  conceived.  We 
have  nothing  but  pity  mingled  with  boredom  for 
the  endless  disputes  of  the  Scholastics  on  the  subject 
of  the  unity  or  the  plurality  of  the  substantial 
forms  in  animal  species.  We  know,  in  fact,  that 
nothing  but  individuals  really  exist,  and  that,  to 
the  static  abstractions  of  our  mind  regarding  these 
genera  and  species,  nothing  invariable  and  essential 
corresponds,  beyond  a  mere  bond  of  relationship 
and  a  family  resemblance  between  the  individuals 
that  we  range  in  the  same  class.  The  question  of 
knowing  whether  a  body  is  at  rest  or  in  absolute 
motion  is,  according  to  Einstein,  another  example 

1  H.  PoincarS,  Dernieres  pensees,  p.  196. 


INTRODUCTION  XI 

of  a  pseudo-problem.  There  exists  no  absolute 
space  which  might  serve  as  a  privileged  reference 
system;  there  exist  merely  bodies  at  rest  or  in 
motion  relatively  to  one  another. 

It  is  a  metaphysical  problem  of  the  same  kind 
that  arises  from  the  fundamental  dualism  between 
ponderable  matter  and  imponderable  energy,  which 
classical  physics  uses  for  the  basis  of  an  explanation 
of  the  world  and  which  gives  place  to  two  principles 
of  invariance,  the  principle  of  the  conservation  of 
mass  and  the  principle  of  the  conservation  of 
energy.  There  is  a  radical  difference  of  character 
between  these  two  components  of  all  phenomena  of 
nature,  matter  and  energy;  matter  alone  is  endowed 
with  mass,  with  weight  in  proportion  thereto,  and 
with  structure;  energy  has  no  inertia,  no  weight,  and 
no  structure.  Therefore  how  is  it  to  be  conceived 
that  an  imponderable  noncorpuscular  agent  that  has 
no  distribution  in  space  capable  of  representation 
can  be  applied  to  a  body  with  both  mass  and 
inertia,  and  possessing  a  definite  shape,  and  act 
on  it  to  the  point  of  deforming  or  moving  it? 
How,  for  example,  can  luminous  radiation,  if  it  is 
destitute  of  mass,  exert  a  repulsion  in  one  direction 
on  the  source  which  emits  it  and  an  impulse  on  the 
opaque  body  absorbing  it,  as  if  it  represented 
momentum ;  how,  in  other  words,  if  it  -is  deprived  of 
inertia,  can  it  behave  like  a  material  projectile 
which  exerts  a  recoil  pressure  on  the  fire-arm  which 
throws  it  and  a  ballistic  action  on  the  obstacle 
which  it  strikes?  And  if  energy  possesses  some 


Xll  INTRODUCTION 

inertia  how  can  it  accumulate  without  effect  on  a 
body,  like  electric  energy,  without  the  mass  of  this 
body  increasing?  This  is  the  metaphysical  problem 
of  the  mutual  action  of  energy  and  matter.  If 
one  assimilates  mental  labor  to  a  kind  of  energy 
sui  generis,  the  metaphysical  problem  of  the 
relations  between  mind  and  body  presents  itself 
as  a  special  case  of  the  foregoing. 

Vain  attempts  have  been  made  to  reduce  one  of 
the  two  terms  placed  in  contrast  to  the  other  by  the 
dualistic  theory,  in  order  to  escape  the  problem  of 
their  mutual  action;  these  monistic  attempts  have 
merely  served  to  shift  the  problem  by  substituting 
new  difficulties  for  the  one  that  they  attempted  to 
overcome. 

All  this  became  quite  different  as  soon  as  the 
theory  of  relativity  of  Einstein  and  the  theory  of 
quanta  of  Max  Planck  led,  if  not  to  a  complete 
rejection  of  the  fundamental  dualism  of  matter 
and  energy,  at  any  rate  to  an  approach  of  the  two 
terms  by  assigning  to  them  such  common  properties 
as  to  render  their  relations  intelligible.  Thus  these 
theories  confer  on  energy  inertia,  weight  in  propor- 
tion thereto,  and  even  a  certain  kind  of  structure. 
Consequently,  radiation  represents  electromagnetic 
momentum  and  may  be  properly  likened  to  a  ma- 
terial projectile.  The  pressure  of  radiation  ceases 
to  be  incomprehensible  and  to  give  rise  to  the  vexa- 
tious metaphysical  problem  of  the  action  of  the 
imponderable  on  the  ponderable. 

Not  only  does  the  inertia  of  energy,  which  as  late 


INTRODUCTION  Xlll 

as  1913  Brillouin1  described  as  a  "  paradoxical 
fancy/7  relieve  us  from  the  drawbacks  of  such  a 
problem,  but  it  satisfies  our  inherent  need  of  uni- 
fication by  absorbing  the  principle  of  the  conserva- 
tion of  mass  into  the  more  general  one  of  the 
conservation  of  energy  and  by  extending  the  law 
of  Newtonian  attraction  to  radiant  energy.  More- 
over the  fundamental  formula  E  =  mV2  leads  to  the 
following  important  result:  it  permits  the  evalua- 
tion of  the  internal  energy  of  a  gram  of  matter 
at  the  absolute  zero  for  an  observer  at  rest,  an 
energy  which  is  no  less  than  that  of  3  million  kilo- 
grams of  coal. 

The  weight  of  energy,  which,  according  to  the 
experiments  of  Eotvos,  is  proportional  to  its  inertia, 
furnishes,  as  Langevin  has  shown,  a  natural  inter- 
pretation of  the  discrepancies  in  Prout's  law  of 
atomic  weights.  It  is  the  origin  of  the  theory  of 
gravitation  of  Einstein  based  on  the  generalized 
principle  of  relativity.  The  practical  interest  of 
this  theory  is  that  it  leads  to  a  successful  calculation 
of  the  secular  anomaly  of  the  perihelion  of  Mercury, 
and  to  the  correct  interpretation  of  the  shift  of 
Fraunhofer's  lines  in  the  solar  spectrum  as  compared 
with  those  from  a  terrestrial  source,  observed  by 
Fabry  and  Buisson.  But  its  essential  advantage 
lies  in  the  fact  that  it  excludes  from  the  domain  of 
physics  those  metaphysical  entities  that  are  still 
encumbering  it,  such  as  the  absolute  space  and  the 

1  Brillouin,  Propos  sceptiques  au  sujet  du  principe  de  relativite 
(Scientia,  Janvier  1913,  p.  23). 


XIV  INTRODUCTION 

privileged  axes  of  Newton  and  their  successors,  the 
body  alpha  of  Neumann  and  the  stationary  ether 
of  the  opticians.  Psycho-physiology  teaches  us 
with  respect  to  this  point  that  our  senses  perceive 
merely  relative  variations  in  the  external  world 
without  ever  detecting  an  absolute  change.  Ein- 
stein has  reconciled  natural  philosophy  with  the 
requirements  of  epistemology  by  showing  that  it  is 
possible  to  put  the  equations  of  physics  into  a  form 
which  is  generally  invariant  with  respect  to  all 
changes  of  coordinate  axes.  By  making  use  of 
the  absolute  differential  calculus  he  has  shown  that 
it  is  thus  possible  to  substitute  for  coordinate  equa- 
tions intrinsic  equations  expressed  in  terms  of 
tensor  equalities  in  order  to  have  in  the  terminology 
of  the  physical  laws  the  magnitudes  characteristic 
of  the  gravitational  field;  or,  putting  it  more  exactly, 
to  regard  the  physical  laws  as  relations  between  the 
quantities  characteristic  of  the  gravitational  field 
and  the  quantities  characteristic  of  the  special 
phenomena  to  be  studied. 

Lastly,  free  radiation  seems  to  possess  structure. 
The  law  of  energy  distribution  in  the  spectrum  of 
the  black  body  and  the  study  of  the  specific  heats 
of  solids  at  low  temperatures  lead  to  the  belief  that 
the  energy  exchanges  between  material  systems  by 
means  of  radiation  take  place  in  sudden  jumps, 
according  to  integral  multiples  of  elementary  in- 
divisible quantities,  veritable  energy  atoms,  called 
quanta.  The  discontinuity  of  emission  and  ab- 
sorption of  radiation  paves  the  way  for  the  idea  of  a 


INTRODUCTION  XV 

discontinuous  distribution  of  radiant  energy  in  the 
front  of  transverse  light  waves.  This  follows 
necessarily  from  the  interpretation  of  certain  phe- 
nomena such  as  the  photo-electric  effect  and  the 
production  of  rays  by  the  impulse  of  secondary 
cathode  rays  or  X-rays.  Consequently  radiation 
appears  no  longer  to  be  a  form  of  energy  propagated 
after  the  manner  of  continuous1  waves  through  a 
hypothetical  stationary  medium,  Maxwell's  dielec- 
tric ether,  but  as  expelled  into  space  in  the  form  of 
discrete  units  with  a  uniform  velocity  in  a  constant 
gravity  field.  The  ancient  dualism  of  the  ponder- 
able and  the  imponderable,  of  matter  and  energy, 
becomes  transformed  into  one  of  energy  stabilized 
in  material  structures  of  definite  architecture  and 
free  radiation,  both  of  these  modes  of  energy  being 
endowed  equally  with  inertia,  weight  in  proportion 
thereto,  and  structure.  This  may  then  be  called 
the  materialization  of  energy. 


Philosophy  and  the  New  Physics 

CHAPTER  I 
THE  DUALISM  OF  MATTER  AND  ENERGY 

1.    INTRODUCTION. 

It  is  a  general  truth  that  the  majority  of  philo- 
sophical problems  are  insoluble  because  the  prob- 
lems do  not  properly  exist.  The  subjectivism 
of  our  senses,  the  anthropomorphism  of  our  reason- 
ing by  analogy,  the  substantialistic  tendency  to 
realize  our  ideas  and  to  take  purely  logical  dis- 
tinctions as  objects  lead  us  to  conceive  fictitious 
problems,  or  pseudo-problems,  that  have  no  more 
meaning  than  the  insolubilia  on  which  the  eristics 
of  the  ancient  sophists  or  the  forensic  dialectics  of 
the  theological  schools  of  the  middle  ages  were 
exercised.  To  solve  them  is  always  to  show  that 
they  were  problems  which  have  been  badly  stated. 

One  category  of  these  pseudo-problems  is  derived 
from  the  mental  transformation  of  a  simple  analogy 
into  an  absolute  identity,  or  of  a  partial  difference 
into  a  perfect  contrast.  Having  obtained  certain 
dissimilarities  between  two  classes  of  phenomena, 
we  deliberately  deny  to  those  of  one  class  everything 
that  is  shown  to  belong  to  those  of  the  other;  and 
in  this  perfect  antithesis  the  mind  derives  the  satis- 
faction of  symmetry.  We  hold  this  radical  line  of 


PHILOSOPHY    AND    THE    NEW    PHYSICS 


tb  l:be  the  equivalent  of  reality.  If 
we  begin  to  reflect  on  the  fact  that  these  diametric- 
ally opposed  phenomena  show  mutual  interaction, 
then  the  shock  of  this  possibility  outrages  our 
understanding;  how  can  absolutely  heterogeneous 
agents  be  combined,  and  how  can  they  influence 
each  other?  For  example,  having  supposed  as  a 
fact  that  matter  alone  has  mass,  proportional 
weight,  and  shape;  and  that  force  or  energy  pos- 
sesses no  inertia,  no  weight,  and  no  structure,  then  the 
following  problem  inevitably  arises  :  How  can  an 
imponderable  agent  be  applied  to  and  act  on  a 
ponderable  one,  with  mass  and  inertia,  to  the  point 
of  deforming  it  or  imparting  an  impulse  to  it? 
In  accordance  with  the  adage  of  Leibniz,  "causam 
aequat  effectus"  our  mind  refuses  to  conceive  this 
and  our  imagination  declares  itself  incapable  of 
visualizing  it.  Of  the  same  nature  and  issuing  from 
the  same  origin  is  the  problem  of  the  relations 
between  mind  and  body. 

The  solutions  proposed  for  such  problems  ine- 
vitably reiterate  the  following  theme.  In  a  dog- 
matic period  it  is  declared  that  one  of  the  two  terms 
of  the  antithesis  exists  only  apparently,  the  other 
one  alone  being  reality;  one  tries  to  reduce  the  real 
forces  either  to  thrusts  of  elementary  masses  or  to 
fictitious  forces  of  connection  and  inertia,  or,  in- 
versely, one  sacrifices  the  notion  of  material  mass  in 
order  to  avoid  contemplating  anything  but  force 
centers  that  attract  or  repel  in  a  straight  line, 
according  to  a  certain  power  of  the  distance.  In 


INTRODUCTION  6 

supporting  such  reductions  one  perceives  that  in- 
surmountable difficulties  which  merely  displace  the 
original  antinomy  are  encountered.  The  dogmatic 
period  is  followed  by  the  prudent  agnosticism,  of  a 
positive  period.  It  is  maintained  that  science  is 
merely  descriptive,  and  one  is  content  to  express  the 
laws  that  govern  the  relations  of  the  two  classes  of 
agents  without  seeking  to  penetrate  into  their  nature 
or  the  hidden  mechanism  of  their  interaction;  this  is, 
in  the  case  in  which  we  are  interested,  the  period 
of  Ostwald's  energetics.  Finally  an  experimental 
and  critical  period  arrives;  in  it  the  claims  of  the 
two  terms  under  discussion  to  be  placed  in  antithesis 
are  examined,  and  it  is  then  discovered  that  the  latter 
is  not  well  founded.  On  the  contrary,  it  is  shown  to 
be  true  that  the  two  terms,  taken  to  be  diametrically 
opposite,  enjoy  such  properties  in  common  as 
explain  their  interaction;  energy  appears  to  be  en- 
dowed with  inertia,  weight,  and  structure,  like 
matter.  The  profound  reason  for  the  lack  of  success 
of  the  preceding  attempts  at  reduction  is  accounted 
for,  and  the  metaphysical  problem,  thus  removed 
unexpectedly,  vanishes  of  itself. 

2.    THE  DUALISTIC  THEORY. 

A  superficial  view  of  the  external  world  leads  to  a 
classification  of  the  agents  found  in  it  into  two  quite 
distinct  categories.  In  the  first  place,  there  are 
ponderable  bodies,  endowed  with  mass,  weight,  and 
structure,  the  aggregate  of  which  constitutes  matter; 
in  the  second  place,  there  are  imponderable  forces, 


4  PHILOSOPHY    AND    THE    NEW    PHYSICS 

divested  of  inertia,  weight,  and  structure,  the  aggre- 
gate of  which  constitutes  energy.  Take  a  piece  of 
matter  and  make  it  undergo  all  the  possible  physical 
and  chemical  transformations,  such  as  motions;  sub- 
divisions and  recompositions;  expansions  and  com- 
pressions; electrification;  magnetization;  changes 
of  state;  and  chemical  combinations.  There  exists 
an  invariant  with  respect  to  this  group  of  physico- 
chemical  transformations;  that  is,  a  certain  coef- 
ficient characteristic  of  the  individuality  of  this 
piece  of  matter  which  remains  invariable  and  un- 
changed: this  is  its  mass.  The  mass,  therefore, 
serves  for  measuring  a  portion  of  matter  so  well 
that  matter  and  mass  appear  to  be  synonyms. 
Lavoisier  established  the  indestructibility  of  matter 
by  showing,  by  means  of  accurate  weighing,  the 
conservation  of  mass.  A  certain  amount  of  energy 
is,  because  of  the  principle  that  different  forms  of 
energy  are  equivalent,  measured  by  the  amount  of 
mechanical  work  into  which  it  may  be  converted; 
and  experiment  proves  that,  in  an  isolated  system, 
the  amount  of  energy  is  constant.  This  is  summar- 
ized by  a  classical  passage  of  Robert  Mayer:1 
"  Nature  presents  two  categories  of  agents  between 
which  experiment  shows  an  insurmountable  barrier 
to  exist.  The  first  category  comprises  agents  havi  ng 
the  properties  of  being  ponderable  and  impenetrable : 
these  are  forms  of  matter;  the  second  comprises 
agents  lacking  these  properties:  these  are  forces 

1  Robert  Mayer,  Annalen  der  Pharmacie  und  Chemie,  von  Lie- 
big  und  Wohler,  1842. 


DUALISTIC    THEORY  5 

called  imponderables  on  account  of  the  negative 
property  which  characterizes  them.  Forces  are  in- 
destructible, variable  and  imponderable  objects." 

Matter  and  energy  being  equally  indestructible 
and  radically  heterogeneous,  neither  can  grow  at 
the  expense  of  the  other  or  decrease  to  its  gain. 
Matter  must  return  the  energy  to  an  amount  equiva- 
lent to  what  has  been  given  to  it  in  another  form. 
It  serves  to  store  it  up  like  a  sponge  that  has  been 
saturated  with  water  and  is  then  in  turn  pressed 
dry;  but,  in  contrast  with  the  analogous  case,  the 
presence  of  energy  in  matter  does  not  increase  its 
mass  since  energy  is  imponderable.  Matter  is  the 
natural  receptacle  of  energy,  which  does  not  exist 
independently  of  it.  Mass  of  ponderable  bodies 
and  imponderable  energy  are  conserved,  each  on  its 
own  account  like  two  distinct  worlds,  one  super- 
imposed on  the  other,  which  completely  penetrate 
without  knowing  each  other  and  without  consenting 
to  reciprocal  exchanges.  This  is  what  a  recent 
author  expresses  as  follows:1 

"The  world  where  we  live  is  in  reality  a  double 
world,  or  rather  it  consists  of  two  distinct  worlds, 
one  of  which  is  the  world  of  ^matter,  the  other  the 
world  of  energy.  Copper,  iron,  carbon,  that  is 
the  world  of  matter.  Mechanical  work,  heat,  these 
are  forms  of  energy.  Each  of  these  two  worlds  is 
governed  by  a  law  of  conservation.  Matter  can  not 
be  created  nor  destroyed ;  energy  can  not  be  created 
nor  destroyed." 

1  Paul  Janet,  Legons  d'Electricite,  2  Edition,  pp.  2  and  5. 


6  PHILOSOPHY    AND    THE    NEW    PHYSICS 

"  Matter  or  energy  may  appear  in  a  large  number 
of  forms,  without  matter  ever  changing  into  energy 
or  energy  into  matter." 

"We  can  no  more  conceive  of  energy  without 
matter  than  of  matter  without  energy." 

This  dualistic  doctrine  of  the  universe  rests  on 
the  following  principle : 

Matter  alone  is  endowed  with  mass,  weight, 
and  structure;  energy  has  no  mass,  no  weight, 
and  no  structure. 

This  principle  is  supposed  to  be  founded  on 
the  following  propositions  which  we  shall  hereafter 
call  the  postulates  of  the  theory: 

1.  Energy  is  never  localized  outside  of  matter. 

2.  The  presence  of  energy  in  a  body  does  not 
increase  the  inertia  of  the  latter. 

3.  The  presence  of  kinetic  inertia  in  particular, 
that  is,  the  state  of  motion  of  a  body,  does  not 
increase  its  mass. 

4.  Absorption  or  emission  of  energy  by  radiation 
neither  increases  nor  diminishes  the  mass  of  a  body. 

5.  The  mass  of  bodies  being  indestructible,  the 
principle  of  the  conservation  of  mass  is   distinct 
from  the  principle  of^the  conservation  of  energy. 

3.  THE  DIFFICULTIES  OF  THE  DUALISTIC  THEORY  AND 
THE  CHECK  GIVEN  TO  THE  MONISTIC  ATTEMPTS 
AT  REDUCTION. 

The  fundamental  dualism  of  matter  and  energy 
leads  to  insurmountable  difficulties.  How  can  im- 
material forces  act  on  inert  bodies  so  as  to  move 


MONISTIC    ATTEMPTS 

them  and  verify  the  ancient  formula  mens  agitat 
moleml  How  can  luminous  radiation  if  it  is  devoid 
of  mass,  exert  a  repulsion  in  one  direction  on  the 
material  source  emitting  it,  and  a  propulsion  on  an 
opaque  body  absorbing  it,  as  if  it  represented  an 
amount  of  momentum;  how,  in  other  words,  can  it, 
if  it  is  destitute  of  inertia,  behave  like  a  material 
projectile,  which  exerts  a  recoil  pressure  on  the 
fire-arm  which  throws  it  and  a  ballistic  action  on 
the  obstacle  which  it  strikes?  And  if  energy  pos- 
sesses some  inertia,  how  can  it  accumulate  like 
electric  energy  on  a  body  to  a  considerable  amount, 
without  the  mass  of  the  latter  being  found  to  have 
grown  in  some  manner?  In  the  presence  of  such  an 
antinomy  our  understanding  feels  outraged  and 
our  imagination  declares  itself  inadequate. 

Furthermore  there  are  the  attempts  at  reduction, 
by  the  monists,  coming  one  after  another  and  seek- 
ing to  resolve  this  initial  contradiction  by  reducing 
one  of  the  two  terms  of  the  antithesis  to  a  mere 
semblance  of  the  other.  But  Stallo,  Hannequin, 
Duhem,  and  Meyerson1  have  shown  that  in  these 
attempts  the  difficulty  is  simply  shifted. 

The  first  attempt,  in  time,  is  that  of  the  atomists, 
whose  fate,  from  Leucippus  and  Democritus  to  Huy- 
gens  and  the  Bernouilli  brothers,  is  especially  note- 
worthy. It  consists  in  reducing  the  supposedly 

1  Stallo,  The  concepts  of  modern  physics.  Hannequin, 
Essai  critique  sur  1'hypothese  des  atomes  dans  la  science  contem- 
poraine. — Duhem,  L' Evolution  de  la  Mecanique. — Meyerson, 
Identite  et  Realite. 


8  PHILOSOPHY    AND    THE    NEW    PHYSICS 

occult  notion  of  force  to  the  clear  and  distinct 
one  of  mass;  and  for  this  purpose  seeks  to  give 
account  of  all  phenomena  by  the  motion  of  elemen- 
tary masses,  indivisible  and  indeformable,  impinging 
on  one  another.  But  if  the  atoms  are  rigid,  trans- 
mission of  motion  through  impact  is  impossible;  if 
they  are  elastic,  they  are  then  deformable  and  com- 
posed of  parts,  which  is  contrary  to  the  hypothesis 
and  implies  forces  of  cohesion  and  elasticity;  this 
inevitable  dilemma  leads  to  shipwreck.  Moreover 
Hertz,1  in  his  posthumous  mechanics,  aims  at  ex- 
plaining everything,  not  by  atoms,  but  by  articulated 
systems,  by  masses  subject  to  firm  bonds  which 
must  conform  to  a  single  law :  every  isolated  system 
traverses  with  constant  speed  a  trajectory  of  least 
curvature.  What  we  take  as  real  forces  are  fic- 
titious forces  of  connection,  due  to  the  presence 
of  bodies  that  we  do  not  perceive,  or  fictitious 
forces  of  inertia,  arising  from  a  motion  that  we  do 
not  suspect.  For  example,  anyone  who,  pulling  a 
body  tied  to  another  by  an  invisible  cord,  saw  the 
second  move  forward,  would  believe  in  a  mutual  at- 
traction of  the  two  bodies,  while  it  would  be  the 
case  of  a  force  of  connection  produced  by  a  hidden 
mass;  and  anyone  who,  not  knowing  the  motion  of 
rotation  of  a  gyroscope,  encountered  an  active  re- 
sistance to  an  attempt  to  produce  a  deviation  of  its 
axis,  would  believe  that  a  real  couple  tended  to 

1  Hertz,  Die  Principien  der  Mechanik  in  neuem  Zusammenhang 
dargestellt  (Ges.  W.  Vol.  Ill)  Johann  Ambrosius  Earth,  Leipzig 
1894. 


MONISTIC    ATTEMPTS  9 

maintain  this  axis  in  an  invariable  direction,  while 
it  would  be  a  case  of  a  force  of  inertia  produced  by 
a  hidden  motion. 

Thus  "what  we  are  accustomed/'  says  Hertz, 
"to  denote  by  the  names  of  force  and  energy  is 
nothing  more  than  the  action  of  mass  or  motion." 
As,  moreover,  nothing  limits  the  motions  and  the 
hidden  .masses  that  may  thus  be  introduced,  it  seems 
as  if  it  were  always  possible  to  give  an  account 
of  the  behaviour  of  natural  phenomena  in  this  man- 
ner. But  this  very  elasticity  is  in  itself  the  cause  of 
sterility.  In  spite  of  all  the  interest  which  is  at- 
tached to  attempts  of  this  kind,  such  as  those  of 
Maxwell  on  electricity,  of  Lord  Kelvin  on  the  gyro- 
static  ether,  and  of  Helmholtz  on  cyclical  systems; 
the  concept  of  Hertz  has  not  led  to  a  single  positive 
result.  Boltzmann1  has  shown  that,  however  great 
the  number  of  masses  and  hidden  motions  one  im- 
agines, and,  however  great,  the  consequent  number 
of  arbitrary  variables  to  which  one  resorts,  it  is  im- 
possible to  represent  the  simplest  phenomenon  in  a 
satisfactory  manner.  Later,  we  shall  find  the 
reason  for  this  lack  of  power  to  be  the  incompati- 
bility of  the  form  which  the  relativity  principle 
imposes  on  physical  laws,  with  the  form  of  the 
equations  of  classical  mechanics  which  govern 
the  displacements  of  the  elementary  masses  of 
the  atomists  and  the  articulated  systems  of  Hertz. 

The  inverse  reduction,  of  mass  to  force,  has  been 

1  Boltzmann,    Anfrage   die   Hertz'   sche    Mechanik   betreffend 
(Wiedemann's  Annalen,  Suppl.  1889). 


10  PHILOSOPHY    AND    THE    NEW    PHYSICS 

the  work  of  Boscovich,  following  Kant.  The  atoms 
lose  all  material  existence,  and  all  spatial  meaning; 
they  are  nothing  more  than  dynamical  points,  or 
force  centers.  These  forces  are  directed  in  the 
straight  line  joining  them,  whence  their  name  of 
central  forces.  They  are  transformed  in  the  nick 
of  time  from  repelling  to  attracting  and  their  in- 
tensity depends  on  a  certain  power  of  the  distance. 
But  if  these  force  centers  are  mathematical  points 
in  space,  how  can  we  imagine  that  a  force  can  apply 
itself  to  them  in  order  to  repel  them  or  attach  itself 
to  them  in  order  to  attract  them?  How  can  these 
entities  of  thought  resist  motion,  and  exhibit  iner- 
tia? "No  arrangement  of  centers  of  force,"  de- 
clares Maxwell,1 "  however  complicated,  can  account 
for  this  fact;  no  part  of  this  mass  can  be  due  to 
the  existence  of  the  supposed  centers  of  force."  It 
seems,  moreover,  that  certain  phenomena,  such  as 
crystallization  and  permanent  deformations,  can 
not  be  explained  if  one  is  limited  to  purely  central 
forces. 

Lastly  Lord  Kelvin's2  concept  of  a  gyrostatic 
non-dynamical  ether,  in  supressing  the  rebellious 
concepts  of  force  and  mass,  has  not  thereby  been 
more  successful.  Reviving  the  ideas  of  Descartes, 
Lord  Kelvin  contemplates  a  perfect  fluid,  homogene- 
ous and  incompressible,  which  fills  all  space.  In 
this  fluid  there  exist  eddy  rings,  which  are  eternal 

1  Maxwell,  Theory  of  Heat,  p.  86. 

2  Cf.   Tait,  Lectures  on  Some  Recent  Advances  in  Physical 
Science. 


MONISTIC    ATTEMPTS  11 

and  can  neither  be  cut  nor  penetrated  and  which 
play  the  part  of  vortex  atoms.  Forces  are  due  to 
pressure  of  the  medium  between  these  vortices. 
But,  as  Maxwell1  remarks,  one  gets  no  sight  of  the 
invariable  element  which  one  would  agree  to  con- 
sider as  the  mass  of  the  atom.  He  contemplates 
therefore  a  pure  motion  in  pure  space  without 
moving  object,  kinetic  energy  being  half  of  the 
product  of  the  square  of  a  velocity  by  a  zero  mass, 
which  is  absurd. 

Thus  the  mechanistic  theory  of  the  atomists, 
the  kinematic  theory  of  Hertz,  the  dynamical  theory 
of  Boscovich,  and  the  non-dynamical  theory  of 
Lord  Kelvin,  have  conclusively  failed  in  their 
attempt  to  reduce  either  force  to  mass  or  mass  to 
force.  The  efforts  of  this  youthful  dogmatism  are 
followed  by  the  prudent  attitude  of  reserve  of  a 
school  of  physics  that  takes  no  interest  in  a  me- 
chanism explaining  the  phenomena,  but  describes 
simply,  in  its  equations,  the  relations  which  connect 
the  simultaneous  variations  of  directly  measurable 
physical  quantities;  a  kind  of  physics  in  which 
there  are  many  integral  quantities,  but  no  atoms. 

Rankine  and  Ostwald  have  both  remarked  that 
these  directly  measurable  physical  quantities  are 
always  quantities  of  energy.  "To  establish  such 
relations  between  measurable  quantities  that,  some 
of  these  quantities  being  given,  the  others  may  be 
deduced,  is  the  entire  task  of  science.  Hereafter 
there  is  no  need  of  troubling  ourselves  about  forces, 

1  Maxwell,  Art.  "Atom"  in  Encyclopedia  Britannica. 


12  PHILOSOPHY    AND    THE    NEW    PHYSICS       . 

the  existence  of  which  we  cannot  prove,  exerted 
between  atoms  that  we  know  nothing  of,  but  we  are 
concerned  with  quantities  of  energy  put  into  play 
by  the  phenomenon  under  investigation  .  .  . 
All  the  equations  that  connect  one  phenomenon 
with  one  or  several  of  a  different  kind  are  neces- 
sarily equations  between  quantities  of  energy; 
there  can  be  no  others,  for,  apart  from  time  and 
space,  energy  is  the  only  quantity  common  to  all 
kinds  of  phenomena."1 

4.  OSTWALD'S  ENERGETICS. 

From  OstwakTs  energetics,  the  genesis  of  which 
we  have  just  traced,  we  may  accept  the  following 
two  propositions: 

(1)  Of  the  external  reality  we  know  only  changes 
of   energy   and   all   physical   phenomena   may   be 
described  in  terms  of  energy. 

(2)  In  particular  a  body  is  only  a  'complex  of 
indissolubly  associated  energies,  so  that  the  concept 
of  matter  becomes  included  in  the  more  general 
one  of  energy,  and  the  principle  of  conservation  of 
mass  is  absorbed  by  the  more  universal  one  of 
conservation  of  energy. 

The  first  proposition  is  easy  to  justify.  In  the 
first  place  by  psycho-physiology:  The  apparatus 
of  our  senses  is  set  into  action  only  by  energy 
changes  between  it  and  the  external  world.  The 
energy  of  the  physico-chemical  agents  that  im- 

1  Ostwald,  Zur  modernen  Energetik,  (Scientia,  1907,  number 
1). 


ENERGETICS  13 

presses  it  is  transformed  into  nervous  energy, 
which  itself  is  transformed,  in  the  cortical  centers, 
into  psychic  energy  sui  generis.  "If  you  receive  a 
blow  with  a  stick,"  says  Ostwald1  jocularly,  "what 
do  you  feel,  the  stick  or  its  energy?"  The  physical 
phenomena  appear,  on  the  other  hand,  as  reducible 
to  a  condition  of  rest,  transfer  or  transformation 
of  energies  of  different  forms:  kinetic  energy; 
potential  energy  of  position;  radiant  energy;  electric 
energy;  magnetic  energy;  heat  energy;  and  chemical 
energy.  Every  form  of  energy  is  the  product  of 
two  factors,  an  intensity  factor  and  a  quantity 
factor,  a  variable  of  equilibrium  and  a  variable  of 
condition:  kinetic  energy  is  half  the  product  of 
mass  and  the  square  of  velocity;  gravitational 
energy  is  the  product  of  height  and  weight ;  volume 
energy,  of  pressure  and  volume;  shape  energy  or 
elasticity,  of  force  and  displacement;  electric  energy, 
of  potential  and  charge,  or  of  elctromotive  force 
and  quantity;  heat  energy,  of  temperature  and 
entropy;  chemical  energy  of  thermodynamic  po- 
tential and  the  masses  of  the  constituents. 

The  idea  of  a  body  becomes  reduced  to  that  of  an 
energy  complex:  volume  energy  which  causes  a 
body  to  occupy  a  definite  region  of  space;  energy 
of  motion  which  causes  it  to  possess  a  definite 
capacity  for  kinetic  energy  or  mass;  gravitational 
energy  which  causes  it  to  have  weight.  It  is  neces- 
sary to  add  to  these  three  fundamental  forms  of 

1  W.  Ostwald,  Die  Ubcrwindung  des  wissenschaftlichen  Mate- 
rialismus.  Zeitschr.  f.  phys.  Chem,,  vol.  18,  p.  305,  1895, 


14  PHILOSOPHY   AND    THE    NEW    PHYSICS 

energy  another  which  is  essential  for  solid  bodies, 
namely,  energy  of  shape  or  elasticity,  by  virtue  of 
which  solids  resist  agents  that  tend  to  penetrate  or 
deform  them.  Every  body  possesses,  in  addition  to 
these  energies,  others  in  varying  proportion :  chemi- 
cal, heat,  electric,  and  magnetic  energy.  If  we  ask 
why  energies  of  volume,  motion,  and  gravity  appear 
always  associated  in  material  systems,  the  answer 
is  found  to  be  in  the  very  conditions  of  the  external 
perception.  If  any  one  of  these  three  energies  were 
lacking  in  a  body,  the  latter  would  escape  our  notice. 
A  body  not  possessed  of  volume  energy  would  not 
occupy  space,  it  would  be  imperceptible;  in  the  case 
of  one  not  possessed  of  mass,  an  infinitely  small  im- 
pulse would  give  it  an  infinitely  large  speed  but  it 
would  again  be  imperceptible;  if  not  possessed  of 
weight  it  would  leave  the  earth  and  escape  our  ob- 
servation. The  objects  that  constitute  the  world 
of  our  sense  experiences  must  therefore  necessarily 
possess  these  three  indissolubly  associated  forms 
of"  energy,  the  complex  of  which  expresses  all  the 
positive  contents  of  the  idea  of  matter. 

Two  general  principles  govern  the  states  of  rest, 
transfer,  and  transformation  of  energy.  They  are 
the  principle  of  conservation  of  energy  and  the 
principle  of  degradation  of  energy. 

The  first  rests  on  the  discovery  of  the  mechanical 
equivalent  of  heat  and  its  generalization  for  all 
forms  of  energy.  It  states  that  in  an  isolated 
system  energy  cannot  be  destroyed  or  created  but 
can  merely  pass  from  one  form  into  an  equivalent 


INSUFFICIENCY   OF   ENERGETICS  15 

amount  of  another  form.  The  second  enunciates 
that  all  forms  of  energy  have  a  tendency  to  be  con- 
verted into  heat  and  all  temperatures  to  become 
equal,  and  may  be  also  formulated  thus:  "In 
a  closed  system  the  entropy  always  increases." 
Boltzmann,  by  reducing  the  entropy  to  the  logar- 
ithm of  the  probability  of  a  certain  state,  has  shown 
that  this  principle  is  a  law  of  large  numbers  which 
expresses,  for  very  complex  systems,  the  chance  of 
the  most  probable  states  being  realized.  In  the 
following  we  shall  have  to  refer  to  the  principle  of 
conservation  of  energy  alone. 

5.  THE  INSUFFICIENCY  OF  OSTWALD'S  ENERGETICS 
AND  THE  EXPERIMENTAL  DISCOVERY  OF  THE  IN- 
ERTIA OF  ENERGY. 

In  proposing  his  energetics  as  a  method  of 
exposition,  a  gnosiological  theory,  Ostwald  is  un- 
assailable. He  is  merely  applying  to  physical 
questions  the  positive  method,  as  formulated  by 
Auguste  Comte,  who  was  gratified  to  see  it  applied 
in  the  work  of  Fourier  on  heat ;  that  is,  he  establishes 
the  equations  that  connect  the  simultaneous  varia- 
tions of  measurable  physical  quantities,  without  pre- 
occupying himself  with  the  question  whether  they 
can  be  reduced  to  each  other  qualitatively,  accord- 
ing to  their  real  nature.  However,  by  excluding  alt 
explanatory  theories,  Ostwald  does  not  solve,  but 
eludes,  the  problem  of  knowing  how  an  imponderable 
agent  by  applying  itself  to  a  body  with  mass  and 
inertia  can  impart  to  it  an  acceleration  or  determine 


16  PHILOSOPHY    AND   THE    NEW    PHYSICS 

a  deformation  in  it.  He  condemns  us  to  an  intellec- 
tual asceticism,  a  position  which  the  human  mind  is 
not  satisfied  to  take;  and  that  too  at  the  precise 
instant  when  the  success  of  the  hypothesis  of  elec- 
trolytic ions,  advanced  by  Clausius  and  Svante 
Arrhenius,  rehabilitated  the  more  concrete  theories, 
by  making  it  possible,  through  the  efforts  of  the 
latter,  van't  Hoff,  andOstwald  himself,  to  group  into 
a  coherent  body  of  doctrine  the  aggregate  of  electro- 
lytic, osmotic  and  chemical  properties  of  aqueous 
solutions.  Moreover,  physicists  have  come  by  a 
different  path  to  doubt  the  traditional  antithesis 
between  matter  and  energy  and  to  establish  by 
experiment  the  inertia  of  the  latter. 

The  experiments  of  Faraday  have  demonstrated 
the  localization  of  electric  and  magnetic  energy 
outside  of  conductors  and  magnets,  contrary  to  the 
first  postulate  of  the  dualistic  doctrine.  The  self- 
induction  of  electric  currents  in  the  conductors 
has  revealed  to  them  the  existence  of  a  veritable 
electromagnetic  inertia.  The  discovery  of  con- 
vection currents,  predicted  by  Maxwell,  realized 
by  Rowland,  has  led  them  to  foresee  that,  on  the 
inertia  proper  of  a  charged  particle  in  motion,  there 
must  be  superimposed  a  supplementary  inertia  of 
electromagnetic  origin,  contrary  to  the  second 
postulate  of  the  dualistic  doctrine.  This  inertia,  for 
velocities  exceeding  30,000  km.  per  sec.,  varies  with 
the  velocity.  The  cathode  particles  issuing  from 
Crookes'  tubes  and  the  /3  rays  from  radium,  issuing 
from  the  disintegration  of  the  atom,  have  velocities 


INERTIA    OF    ENERGY  17 

of  just  this  order  of  magnitude.  Experimental 
study  of  the  variations  of  the  electromagnetic 
inertia  as  a  function  of  the  velocity  becomes  here- 
after possible.  Undertaken  by  Kaufmann  and 
Bucherer,  it  shows  the  existence  of  grains  of  resinous 
(negative)  electricity,  or  electrons,  destitute  of 
material  support,  the  mass  of  which  is  solely  of 
electromagnetic  origin  and  varies  as  a  function  of 
velocity.  Hence  we  have  here  a  form  of  energy, 
electric  energy,  that  is  endowed  with  mass  and  struc- 
ture, contrary  to  the  fundamental  principle  of  the 
dualistic  doctrine.  The  relativity  principle,  which 
results  from  the  failure  of  all  attempts  to  demonstrate 
the  absolute  movement  of  a  system  by  experience 
within  this  system,  then  intervenes  to  show  that 
all  bodies  behave  during  translation  as  if  their 
mass  were  solely  electro-magnetic,  that  is,  as  if  it 
were  no  more  an  invariable  scalar  quantity,  but  a 
tensor  quantity,  symmetrical  and  variable,  contrary 
to  the  third  postulate  of  the  dualistic  theory. 

Absorption  and  emission  of  radiant  energy  by 
bodies  and  the  pressure  of  radiation  resulting  there- 
from, in  accord  with  the  theoretical  views  of  Maxwell 
and  Bartoli  and  the  experimental  results  of  Lebedew, 
lead,  on  the  other  hand,  to  endowing  electromagne- 
tic radiation  with  momentum,  in  order  to  safeguard 
the  relativity  principle  and  Newton's  principle  of 
action  and  reaction  or  its  corollary,  that  of  the 
conservation  of  momentum  in  an  isolated  system. 
But  momentum  implies  moving  mass.  Radiant 
energy,  therefore,  has  mass;  and  all  other  energy, 


18  PHILOSOPHY    AND    THE    NEW    PHYSICS 

no  matter  what  its  form,  being  convertible*  into 
energy  of  radiation,  possesses  a  coefficient  of  inertia. 
The  mass  of  a  material  system  changes  through 
absorption  or  radiation  of  energy,  since,  in  the  first 
case,  it  is  increased  by  all  the  inertia  of  the  absorbed 
radiation,  and,  in  the  second  case,  diminishes  by 
the  amount  appertaining  to  the  radiation  emitted. 
From  the  formulae  it  follows  that,  if  we  take  the 
velocity  of  light  as  unity,  the  inertia  of  a  material 
system  is  the  measure  of  its  internal  energy.  The 
mass  ceasing  to  be  invariable,  the  principle  of  the 
conservation  of  mass  becomes  merged  in  the  princi- 
ple of  the  conservation  of  energy,  as  previously  con- 
ceived by  Ostwald,  and  contrary  to  the  last  postu- 
late of  the  dualistic  theory. 

Matter  and  energy  are  endowed  equally  with 
inertia  and,  according  to  the  experiments  of  Eotvos 
on  the  proportionality  of  inert  mass  and  gravita- 
tional mass,  with  weight  in  proportion  thereto. 
There  still  persists  the  opposition  between  matter, 
characterized  by  its  structure  (the  number  and  na- 
ture of  the  electrons,  and  possibly  also  the  positive 
remainders,  of  which  it  is  composed)  and  the  pos- 
sibility of  moving  with  velocities  varying  from  zero 
to  that  of  light,  and  radiation  which  moves  uni- 
formly with  the  speed  of  light.  This  opposition 
becomes  weaker  because  of  the  quantum  theory. 
This  theory  shows  that  radiant  energy  is  not  uni- 
formly propagated  in  a  hypothetical  medium,  but  is 
emitted  into  space  in  the  form  of  discrete  units. 

The    metaphysical    problem    of    the    action    of 


INERTIA    OF    ENERGY  19 

an  imponderable  on  a  ponderable,  of  force  on  mat- 
ter, disappears  as  a  pseudo-problem,  born  of  an 
artificial  antithesis  between  matter  and  energy 
assumed  at  the  outset.  On  account  of  the  inertia 
of  the  latter,  there  is  no  more  difficulty  in  under- 
standing, for  example,  the  pressure  on  the  matter 
absorbing  it,  since,  being  endowed  with  momentum, 
light  behaves  strictly  like  a  material  projectile 
striking  an  obstacle. 

Thus,  as  already  stated,  matter  was  errone- 
ously opposed  to  energy,  by  denying  to  the  latter 
everything  that  had  been  found  to  belong  to  the 
former.  This  led  to  a  fundamental  antinomy  which 
gave  rise  to  a  pseudo-problem.  The  monistic  at- 
tempts to  reduce  one  of  the  terms  of  the  antithesis 
to  the  other  have  merely  served  to  shift  the  diffi- 
culty without  relieving  it,  and  Ostwald's  energetics 
merely  to  escape  the  problem  without  solving  it. 
The  recent  discoveries,  however,  by  opening  up  a 
field  of  experiment  of  an  extent  beyond  all  expecta- 
tion, such  as  the  possibility  of  having  at  our  dis- 
posal velocities  approaching  that  of  light,  have 
led  physicists  to  revise  the  primitive  classification 
of  natural  agents  into  ponderables  and  imponder- 
ables. It  has  been  discovered  that  this  Classification 
was  not  well  founded,  that  the  admitted  anti- 
thesis between  matter  and  energy  was  artificial,  and 
that  these  two  realities,  in  spite  of  differences  which 
forbid  their  confusion,  possess  precisely  the  common 
characteristics  that  permit  the  explanation  of  their 
mutual  action. 


20  PHILOSOPHY    AND    THE    NEW    PHYSICS 

This  result,  essential  for  natural  philosophy, 
is  the  end  of  a  long  line  of  theoretical  reasoning 
and  experimental  verification,  which  unite  conclu- 
sively to  establish  the  following  proposition:  Energy 
is  endowed  with  inertia.  In  order  to  understand 
the  inner  logic  of  this  wonderful  organic  de- 
velopment, it  must  be  followed  without  haste,  step 
by  step.  The  physicists  have  not  found  that  royal 
road  leading  directly  to  the  goal  by  which  Ptolemy  I 
asked  Euclid  to  conduct  him  to  the  comprehension 
of  the  most  transcendent  scientific  truths.  They 
have  not  abandoned  the  old  principles  under  pres- 
sure of  the  new  facts  until  they  had  tried  all  possible 
ways  of  saving  them.  They  have  not  risked  one 
step  forward  without  summoning  an  advocatus 
diaboli  against  themselves.  They  have  been  pru- 
dent in  their  innovations.  Old  mental  habits, 
stabilized  through  long  ages  of  scholasticism,  and 
the  narrow  evidences  offered  by  a  traditional  ra- 
tionalism are  not  got  rid  of  in  a  day;  nor  does  one 
easily  leave  the  beaten  track  of  an  imagination 
which  derives  satisfaction  only  from  the  contempla- 
tion of  solids.  In  particular,  the  consideration  of 
Maxwell's  dielectric  ether,  which  comes  under  the 
category  of  Hertz's  hidden  masses  and  movements, 
has  for  a  long  time,  by  misleading  physicists  into 
attempts  at  mechanical  explanations,  paralyzed 
efforts,  of  which  the  relativity  principle  finally  had 
to  show  the  futility.  Leaving  useless  details  aside, 
we  shall  follow  in  its  essential  curves  the  turnings 
of  the  winding  road  which  has  led  the  physicists  of 


INERTIA    OF    ENERGY  21 

the  new  school  to  a  conception  of  the  universe,  the 
beauty  of  which  is  a  joy  forever.  To  arrive  there 
more  easily  we  shall  at  the  outset  recall  a  certain 
number  of  ideas  and  principles  which  will  be  con- 
stantly used  in  the  sequel. 


CHAPTER  II 
MASS  AND  THE  RELATIVITY  PRINCIPLE 

6.  THE  IDEA  OF  MASS;  EINSTEIN 's  EQUIVALENCE 
PRINCIPLE  AND  NEWTON  's  PRINCIPLE  OF  ACTION 
AND  REACTION. 

In  order  to  show  how  the  idea  of  energy  as  en- 
dowed with  mass  and  weight  in  proportion  thereto 
has  been  arrived  at,  it  is  necessary  to  define  these 
two  ideas  and  to  state  two  principles  which  are 
closely  associated  with  them. 

What  constitutes  the  individuality  of  a  piece  of 
matter  through  all  motions,  divisions,  recomposi- 
tions,  compressions,  expansions,  changes  of  state  and 
chemical  combinations  that  it  undergoes,  is  its  mass, 
which  presents  itself  as  an  invariant  of  the  group  of 
physico-chemical  changes.1  It  is  considered  in 
classical  mechanics  as  an  invariable  scalar  quantity 
that  characterizes  every  piece  of  matter  and  may  be 
defined  in  three  different  ways:  (1)  as  a  coefficient  of 
inertia;  (2)  as  capacity  for  momentum;  (3)  as  capa- 
city for  kinetic  energy.  *  ^ 

As  coefficient  of  inertia,  mass  measures  the  re- 
sistance of  a  body  to  any  action  tending  to  modify 
its  state  of  motion.  Newton  assumes  the  propor- 

1  Cf.  F.  Enriques,  Les  Concepts  fondamentaux  de  la  Science, 
p.  136-144. 

22 


IDEA    OF   MASS  23 

tionality  of  the  force  acting  on  a  body  to  the  change 
in  velocity  per  unit  time  communicated  to  it,  or  the 
acceleration;  therefore  the  quotient  of  force  by 
acceleration  defines  the  mass  of  a  body.  Moreover, 
he  assumes  the  principle  of  the  independence  of  the 
effects  of  a  force,  which  leads  to  the  view  that  the 
mass  of  a  moving  body  is  independent  of  the  veloc- 
ity acquired :  if  a  force  acts  on  a  body  for  a  second, 
starting  from  rest,  and  communicates  to  it  the  veloc- 
ity v,  the  same  force  acting  through  another  second 
will  communicate  to  it  a  second  increment  of  veloc- 
ity equal  to  the  first,  so  that  its  velocity  will  be- 
come 2v}  if  the  same  force  continues  to  act  through  a 
third  second,  the  velocity  will  become  3v  and  so  on. 
Theoretically  a  moving  body  may  be  given  a  veloc- 
ity as  large  as  we  please  by  the  application  of  the 
same  force  a  sufficiently  large  number  of  times. 
Lastly  the  mass  of  a  body  is  independent  of  the 
sense  in  which  the  force  acts,  whether  it  be  parallel 
to  the  direction  of  the  velocity  (tangential  accelera- 
tion) or  at  right  angles  thereto  (normal  acceleration) . 
Mass  may  also  be  defined,  as  was  done  by  Mauper- 
tuis,  by  starting  with  the  idea  of  an  impulse  com- 
municated to  a  body  by  a  force  during  the  time 
element  dt.  This  quantity  is  determined  in  mag- 
nitude and  direction  by  the  product  f-dt;  and  the 
impulse  of  a  body  at  the  instant  t  is  the  geometric 
sum  of  the  elementary  impulses  that,  starting  from 
rest,  have  been  successively  communicated  to  it  by 
the  various  forces  exerted  on  it.  In  virtue  of  the 
law  of  inertia,  matter  tends  to  conserve  its  state  of 


24  PHILOSOPHY   AND   THE    NEW    PHYSICS 

motion;  the  impulse  is  equal  to  the  momentum  of  a 
body,  or  the  product  of  its  mass  by  its  velocity  taken 
in  the  same  direction  as  the  latter;  hence  the  vector 
relation 

g  =  mv. 

Mass  may  therefore  be  defined,  as  capacity  for 
momentum,  by  the  impulse  divided  by  the  velocity 
according  to  the  relation 


Lastly,  the  kinetic  energy  of  a  body  may  be  de- 
fined by  the  total  work  which  had  to  be  expended 
to  bring  the  body  from  rest  into  its  actual  state  of 
motion  without  deforming  it  for  observers  moving 
with  it.  This  leads  in  rational  mechanics  to  the 
relation 

w  =  ^mv2. 

Starting  from  this,  mass  can  be  defined,  as  the 
capacity  coefficient  of  kinetic  energy,  by  the  quotient 
of  twice  the  kinetic  energy  and  the  square  of  the 
velocity 

2w 
™=^ 

These  three  definitions  are  equivalent  in  classical 
mechanics  and  we  shall  have  to  refer  to  each  of 
them  in  succession.  But  we  shall  see  that  in  the 
new  dynamics,  the  dynamics  of  the  electron  and 
of  relativity,  they  cease  to  be  identical  for  velocities 
above  30,000  km.  per  sec.  All  three  lead  to  variable 
values,  functions  of  the  velocity,  following  three 


IDEA    OF    MASS  25 

different  laws  which  make  them  assume  an  infinitely 
large  value  for  the  limiting  speed  of  light  in  a 
vacuum.  The  following  leads  to  a  rejection  of 
Newton's  principle  of  the  independence  of  the 
effects  of  a  force.  If  a  force  acts  for  another 
second  its  effect  will  be  less  than  that  produced 
during  the  first;  it  will  be  still  less  during  the  third 
and  less  in  general  as  the  velocity  already  acquired 
by  the  body  becomes  greater,  since  the  inertia 
increases  step  by  step,  until  it  becomes  infinite  for 
the  speed  of  light.  Lastly  in  the  new  dynamics  the 
acceleration  communicated  to  a  body  by  a  force 
depends  on  the  angle  made  by  the  direction  of  this 
force  with  that  of  the  velocity.  We  must  define  a 
tangential  mass  and  a  transverse  mass,  identical 
with  that  defined  by  Maupertuis,  which  do  not 
behave  symmetrically.  Briefly,  mass  ceases  to  be 
a  constant  scalar  quantity  and  becomes  a  tensor 
quantity,  which  is  variable  and  unsymmetrical.1 
The  idea  of  mass  designates  two  quite  different 
things:  (1)  the  coefficient  of  inertia  of  a  body  which 
measures  its  resistance  to  acceleration,  or  inert 
mass',  (2)  the  coefficient  of  attraction  of  a  body  on 
another  outside  of  it,  according  to  Newton's  law, 
or  gravitational  mass.  How  do  these  two  masses 
behave  with  respect  to  each  other?  Newton  sup- 
posed that  there  was  a  strict  proportionality  be- 
tween the  two  coefficients;  but  that  was  not  proved 

1  On  the  subject  of  symmetry  of  physical  quantities  see  L. 
Rougier,  La  symetrie  des  phcnomenes  physiques  et  le  principe  de 
raison  suffisante  (Rev.  de  Met.  et  Mor.  mars  1917,  p.  165-198). 


26  PHILOSOPHY    AND    THE    NEW    PHYSICS 

experimentally  before  Eotvos1  experiment  with 
a  torsion  balance.  On  the  surface  of  our  globe  all 
bodies  are  immersed  in  two  superimposed  fields 
of  force:  the  field  of  gravity,  which  puts  into  play 
the  gravitational  mass  of  bodies,  and  the  field  of 
the  centrifugal  force,  which  puts  into  play  their 
inert  mass.  The  resultant  of  these  two  actions 
combined  is  the  apparent  weight  of  a  body.  If  the 
two  masses  were  different,  the  resultant,  that  is, 
the  observed  direction  of  vertical,  would  not  be 
exactly  the  same  for  all  bodies:  there  would  not 
be  a  single  vertical  at  one  and  the  same  point. 
That  this  is  not  so  has  been  established  by  Eotvos 
by  the  aid  of  a  torsion  balance  with  an  exactness 
which  excludes  relative  divergencies  of  the  order 
10~7?  so  that  the  exact  coincidence  of  the  two  co- 
efficients may  be  taken  for  granted. 

Einstein2  has  from  this  deduced  the  principle 
of  the  equivalence  of  acceleration  and  gravitation;  the 
effects  produced  on  any  system  by  a  gravitational 
field  are  not  distinguishable  from  effects  produced 
by  a  suitable  state  of  acceleration  of  the  same  system 
when  removed  from  the  action  of  the  field,  or,  what 
comes  to  the  same  thing,  from  those  of  a  system 
referred  to  axes  having  an  accelerated  motion  with 
respect  to  it.  In  order  to  learn  the  action  of 

1  B.  Eotvos,  Math.  u.  naturw.     Ber.  aus  Ungarn,  Vol.  VIII, 
1890;  Beibl,  vol.  XV,  1891,  p.  688. 

2  Einstein,  Ann.  der  Phys.,  1911  p.  898  and  seq.;  1912,  p.  365 
and  seq.;  1914/p.  341  and  seq.;  Zeitschr.  f.  Math.  u.  Phys.,  1913, 
p.  6  and  seq.;  Phys.  Zeitschr.,  1914,  p.  176  and  seq.;  Archives  des 
Sciences  phys.  et  nat.,  1914,  p.  7-12. 


ACTION    AND    REACTION  27 

gravity  on  physical  phenomena  it  will  suffice  to 
study  the  effects  of  acceleration  on  them,  that  is, 
to  examine  the  modifications  that  the  physical  phe- 
nomena undergo  when  passing  from  a  reference  sys- 
tem at  rest,  or  in  uniform  translatory  motion,  to  one 
accelerated  with  respect  to  the  former.  From  this 
Einstein  has  made  the  deduction  that  if  energy  is 
inert  it  has  weight  in  proportion.  We  can  no  longer 
imagine  an  agent  like  the  ether  having  a  certain 
density  and  yet  absolutely  imponderable,  that  is  to 
say,  devoid  of  weight.  Everything  that  is  endowed 
with  mass  must  possess  a  certain  coefficient  of  New- 
tonian attraction  in  proportion  thereto. 

The  idea  of  mass  is  intimately  connected  with 
the  Newtonian  principle  of  instantaneous  equality 
of  action  and  reaction.  Without  attempting  to 
fathom  the  meaning  of  this  principle  or  seeking  to 
find  how  it  is  connected  with  the  definition  of  equality 
of  masses,1  we  shall  restrict  ourselves  to  its  enuncia- 
tion. If  a  material  point  A  acts  on  another  B,  the 
body  B  reacts  on  A,  and  these  two  actions  are 
two  instantaneously  equal  and  oppositely  directed 
forces.  For  example,  the  attraction  exerted  by  the 
earth  on  the  moon  is  at  every  instant  equal  to  and 
oppositely  directed  to  the  attraction  exerted  by  the 
moon  on  the  earth.  It  follows  from  the  principle  of 
the  equality  of  action  and  reaction  that  in  the  case 
of  a  closed  system  the  momentum  g  —  mv  remains 
constant.  If  a  body  through  an  internal  action  calls 

1  Cf.  Mach,  History  of  Mechanics,  p.  210-216.  Enriques,  1.  c., 
p.  144-149. 


28  PHILOSOPHY    AND    THE    NEW    PHYSICS 

forth  the  appearance  of  a  certain  momentum,  count- 
ed as  positive,  by  acting  on  another  body,  it  will 
undergo  a  repulsion  on  the  part  of  the  latter  and 
consequently  take  a  momentum  equal  to  the  first 
and  directed  in  the  opposite  sense  so  as  to  com- 
pensate it.  The  center  of  gravity  of  the  system 
will  remain  at  rest.  The  principle  of  the  conservation 
of  momentum  in  a  system  which  is  subject  to  internal 
actions  only  presents  itself  therefore  as  a  corrollary 
of  the  principle  of  action  and  reaction  and  would 
cease  to  be  exact  at  the  same  time  as  the  former. 

7.    THE  RELATIVITY  PRINCIPLE. 

The  relativity  principle  originated  from  the  nega- 
tive result  of  all  the  attempts  to  show  the  ab- 
solute motion  of  a  material  system  by  experiments 
within  that  system. 

Classical  mechanics  assumed  that  all  mechan- 
ical phenomena  in  a  system  in  uniform  rectilinear 
motion  are  produced  exactly  as  if  the  system  were 
at  rest.  An  observer  enclosed  in  Jules  Verne's 
bomb-shell  could  detect  accelerations  or  rotations 
that  this  shell  undergoes  by  observing  phenomena 
taking  place  inside;  he  could  in  no  way  detect  his 
uniform  translatory  motion.  This  is  no  longer  the 
case  if  he  has  recourse  to  optical  or  electrical  experi- 
ments. The  electromagnetic  theory  introduces  a 
medium  at  rest,  the  ether,  which  transmits  the 
transverse  waves  of  light  with  a  definite  speed,  just 
as  air  transmits  sound  waves.  In  the  case  of  a 
source  of  sound  the  relative  motion  of  the  source -with 


RELATIVITY    PRINCIPLE  29 

respect  to  the  air  can  be  measured  without  revealing 
an  absolute  motion  of  the  source  with  respect  to  the 
ether,  since  air  is  dragged  along  by  the  motion  of 
bodies.  This  is  not  so  in  the  case  of  the  ether.  The 
latter,  if  it  exists,  is  incapable  of  motion,  so  that 
one  might  hope  to  show,  by  electromagnetic  or  opti- 
cal experiments  within  a  system,  the  motion  with 
respect  to  the  ether  of  a  source  of  light  connected 
with  the  system.1 

The  earth  possesses  in  its  annual  motion  a  trans- 
latory  velocity  varying  constantly  by  amounts  as 
high  as  60  km.  per  sec.  for  the  relative  velocities  cor- 
responding to  two  diametrically  opposite  positions  in 
its  orbit,  in  January  and  July,  for  example.  Let  us 
consider  the  optical  experiment  actually  performed 
by  Michelson  in  1881  and  repeated  by  him  and 
Morley  in  1887  the  outline  of  which  is  as  follows. 
Let  three  points  O,  P,  and  P'  be  taken  at  the  vertices 
of  an  isosceles  triangle  with  a  right  angle  at  O.  OP 
corresponds  to  the  direction  of  the  translatory  mo- 
tion of  the  earth,  OP7  is  at  right  angles  thereto;  at  O 
a  glass  plate  is  fixed  inclined  at  45°;  at  the  points  P 
and  P'  mirrors  are  fastened  normally  to  the  two 
directions  OP  and  OP'.  Let  us  assume  that  a  light 
ray  comes  from  a  lens  on  the  line  OP'  produced, 
strikes  the  glass  plate  O  and  there  is  divided  into 
two  rays :  one  will  be  reflected  towards  the  mirror  P, 

1  Cf.  H.  A.  Lorentz,  A.  Einstein,  H.  Minkowski,  Eine  Samm- 
limg  von  Abhandlungen,  Teubner  1913.  Laue,  Das  Relativitats- 
princip,  1911.  P.  Langevin,  Le  temps,  1'espace,  et  la  causalite" 
dans  la  Physique  moderne  (Bull.  Soc.  fr.  de  Philos.  vol..  xii,  1912). 


30  PHILOSOPHY    AND    THE    NEW    PHYSICS 

return  to  O  and  passing  through  the  glass  plate  will 
fall  on  the  lens  L;  the  other  will  pass  through  the 
plate  O,  be  reflected  from  the  mirror  P'  and  be 
superimposed  in  the  lens  on  the  first  ray.  If  the 
apparatus  is  at  rest,  the  paths  OPO  and  OP'O  being 
equal  by  hypothesis,  the  times  t  and  t'  required  to 
traverse  them  will  also  be  equal,  and  the  light  dis- 
turbances brought  by  the  two  rays  to  the  focus  of 
the  lens  will  coincide  in  such  a  manner  as  to  give  a 
maximum  of  light  intensity  at  this  point.  The 
aspect  of  the  interference  fringes  will,  by  reason  of 
symmetry,  remain  the  same  for  any  rotation  what- 
ever of  the  apparatus,  the  locus  of  the  points  P  cor- 
responding to  equal  paths  OP  +  PO  being  a  sphere 
with  its  center  at  O. 

If  the  system  has  a  uniform  translatory  motion  v, 
the  locus  of  the  points  P  corresponding  to  equal 
paths  traversed  by  the  light,  is  no  longer  a  sphere 
about  O  but  an  ellipsoid  of  revolution  flattened  in 
the  direction  of  motion,  the  axis  of  which  in  a  direc- 
tion at  right  angles  to  the  velocity  is  to  that  parallel 

/          v* 
thereto  in  the  proportion  1 :  ij  1  —  ™  v  being  the 

velocity  of  the  instrument,  and  V  being  that  of 
light.  If  the  apparatus  remains  undeformed  while 
passing  from  rest  to  motion  and  if  the  instrument  is 
adjusted  at  the  outset  by  experiment,  so  that  the 
paths  OPO  and  OP'O  are  equal  for  a  given  initial 
position,  the  aspect  of  the  interference  fringes  will 
be  changed  because  a  rotation  through  90°  will 
interchange  the  directions  OP  and  OP'  and  this 


RELATIVITY    PRINCIPLE  31 

change  will  reveal  the  absolute  motion  of  the 
system. 

For  example,  if  the  preceding  experiment  is  made 
on  the  earth,  in  January,  and  the  interchange  of  the 
directions  OP  and  OP'  does  not  bring  about  any 
change  in  the  aspect  of  the  interference  fringes,  we 
might  interpret  this  negative  result  by  saying  that 
the  velocity  of  the  earth  relative  to  the  ether  is 
relatively  insignificant.  Six  months  later  it  will 
have  increased  by  60  km.  per  sec.  and  the  repetition 
of  the  experiment  should  bring  about  an  appreciable 
change  in  the  aspect  of  the  fringes.  Contrary  to 
this  anticipation  the  Michelson-Morley  experiment 
gives  a  negative  result,  and  so  too  do  all  optical  and 
electromagnetic  experiments  undertaken  by  Lord 
Rayleigh  and  Brace,  Trouton  and  Noble,  Rankine 
and  Trouton. 

To  account  for  this  result,  Fitz-Gerald  and  Lor- 
entz  assumed  simultaneously  that  all  linear  dimen- 
sions of  bodies  contract  in  the  direction  of  their 


translation   in   the   ratio   A|   1  —  ™  written  more 

simply  V  1  —  |82.  This  contraction  can  not  be 
ascertained  by  observers  O,  connected  with  the 
moving  bodies,  since  all  measuring  instruments  con- 
tract in  the  same  proportion,  but  it  can  be  by  station- 
ary observers  O0  who  see  it  pass.  Let  us  call  the 
configuration  of  a  moving  body  as  measured  by 
observers  connected  with  it  by  means  of  measuring 
rods  having  the  same  translatory  motion,  its  geo- 
metric configuration;  and  let  us  call  its  kinematic 


32  PHILOSOPHY   AND    THE    NEW    PHYSICS 

configuration  the  configuration  of  the  same  body 
measured  by  observers  at  rest  with  respect  to  it, 
who  observe,  at  the  same  instant  according  to  their 
clocks,  during  its  passage,  different  points  of  its 
circumference,  and  determine  the  position  of  these 
different  points  by  means  of  measuring  rods  grad- 
uated at  rest;  the  kinematic  configuration  will  not 
be  identical  with  the  geometric  configuration  ,  it  will 
differ  from  it  by  a  contraction  in  the  ratio  Vl  —  /32. 
In  the  reasoning  that  has  just  led  us  to  an- 
ticipate a  change  in  the  aspect  of  the  fringes  as 
a  result  of  the  rotation  of  Michelson's  apparatus, 
we  have  assumed  the  distances  OP  and  OPf  to  be  in- 
variable during  this  rotation.  According  to  Lor- 
entz's  hypothesis  the  distance  OP',  originally  at 
right  angles  to  the  direction  of  motion,  will,  for 
observers  00  at  rest  who  see  the  instrument  pass, 
contract  during  the  rotation  and  become 
OP  =  ' 


while  inversely  the  distance  OP,  originally  parallel 
to  this  direction  will  expand  in  the  inverse  ratio 
and  become 

OP'  =    2L- 

VI  -  P2' 

so  that  the  equality  of  the  original  times  of  travel 
ti  and  ~t2  will  carry  with  it  the  equality  of  the  later 
times  ti  and  tz. 

As  a  consequence  of  the  Lorentz  contraction 
spherical  bodies  become  flattened  ellipsoids  in  the 
ratio 


RELATIVITY    PRINCIPLE  33 

We  shall  have  to  use  this  result  in  the  dynamics  of 
the  electron. 

The  negative  result  of  experiments  undertaken 
to  discover  the  absolute  motion  of  a  system  with  re- 
spect to  the  ether  has  led  physicists  to  generalize 
the  relativity  principle  assumed  in  rational  mechan- 
ics for  mechanical  phenomena: 

Given  different  groups  of  observers,  00  and  0\,  one 
of  which  is  in  a  state  of  uniform  motion  with  respect 
to  the  other,  the  laws  of  nature  will  be  exactly  the  same 
for  the  different  groups  of  observers.  This  principle 
may  also  be  stated  thus:  the  form  of  the  equations 
expressing  the  laws  of  phenomena  within  a  system 
does  not  change  if  they  are  referred  successively  to  a 
reference  system  at  rest  and  then  to  a  second  system 
having  a  uniform  translatory  motion  with  respect  to 
the  former. 

In  order  to  see  the  meaning  of  the  relativity 
principle  thus  extended  to  all  natural  phenomena  in 
the  case  of  uniform  translatory  motion,  it  will  be 
best  to  compare  it  with  the  principle  of  relativity 
used  in  geometry  and  mechanics. 

In  Euclidean  geometry  we  assume  that  the  shape 
and  the  dimensions  of  a  figure  do  not  depend  on  its 
absolute  position  in  space:  they  remain  unchanged 
for  all  displacements  that  it  undergoes  and  this  is 
what  constitutes  the  relativity  of  space.  We  may 
express  this  by  saying  that  if  the  same  figure  be 
referred  successively  to  different  systems  of  axes 
00  and  0i,  the  equations  of  transformation  that 
permit  us  to  pass  from  the  first  system  to  the  second, 


34  PHILOSOPHY    AND    THE    NEW    PHYSICS 

form  a  group,1  called  an  Euclidean  group,  in  which 
the  form  of  the  equations  that  translate  the  proper- 
ties of  geometrical  figures  is  an  invariant.  Geome- 
try is  nothing  but  the  study  of  the  structure  of  the 
Euclidean  group,  which  is  identical  with  the  group 
of  orthogonal  substitutions. 

In  rational  mechanics  we  assume  that  the  me- 
chanical phenomena  taking  place  in  an  isolated 
system  do  not  depend  on  its  state  of  rest  or  of  uniform 
translatory  motion:  this  constitutes  the  relativity 
of  motion.  We  may  express  this  by  saying  that  if 
we  successively  refer  the  same  mechanical  system 
to  a  reference  system  00  at  rest  with  respect  to  it, 
and  then  to  a  system  0\  in  uniform  translatory 
motion  with  respect  to  the  former,  the  equations  of 
transformation  that  permit  us  to  pass  from  00  to  0\ 
form  a  group,  called  a  Galilean  group,  in  which  the 
form  of  the  equations  of  classical  mechanics  is  an 
invariant.  In  the  simplest  case  we  would  have  for 
such  a  transformation  of  the  space  coordinates  of 
the  first  system  with  the  axes  x,y,z,  into  those  of  the 
second  x',  yf,  zf 

x  =  x'  —  vt 

V  =  y'y 

z  =  z', 

where  v  is  the  velocity  of  translation  of  00  with 
respect  to  0\. 

1  Given  an  aggregate  of  transformations  we  say  they  form  a 
group,  if  the  product  of  any  two  of  these  transformations  and  the 
inverse  transformation  of  any  transformation  still  form  part  of 
this  aggregate. 


RELATIVITY    PRINCIPLE  35 

We  have  just  seen  that  in  physics  all  phenomena 
whatever  taking  place  within  a  system  are  independ- 
ent of  its  state  of  rest  or  of  uniform  translatory 
motion,  and  this  constitutes  the  relativity  of  all 
natural  phenomena.  This  may  be  expressed  by 
saying  that  if  we  refer  successively  the  same  phys- 
ical system  to  a  reference  system  00  at  rest  with 
respect  to  it  and  then  to  a  system  Oi  in  uniform 
translatory  motion  with  respect  to  the  first,  the 
equations  of  transformation  that  permit  us  to  pass 
from  00  to  Oi  form  a  group,  called  a  Lorentz  group. 
Lorentz's  equations  of  electromagnetism  are  an 
invariant  of  this  group.  In  the  simplest  case  of  a 
translatory  motion  of  the  reference  system  0± 
parallel  to  the  rr-axis,  the  transformation  of  space 
and  time  coordinates  of  the  first  system  with  the 
axes  x,  y,  z,  t  into  the  second  x',  y' ',  2',  £',  will  be 
expressed  by  the  four  relations 

x  —  vt  v 


x'  = 


where  0  =  y,  and  where  v  represents  the  relative 

velocity  of  Oi  with  respect  to  00  and  V  the  velocity 
of  light,  which  is  the  same  in  all  directions. 

Minkowski  has  given  a  very  elegant  geometric 
interpretation  of  the  principles  of  relativity  in  a 
four-dimensional  space.  He  substitutes  in  place  of 
the  Galilean  reference  systems  formed  by  three 
axes  at  right  angles  in  the  Euclidean  three-dimen- 
sional space,  much  more  general  systems  formed  by 


36  PHILOSOPHY    AND    THE    NEW    PHYSICS 

four  axes  at  right  angles  in  four  dimensional  space, 
in  which  time  plays  the  part  of  a  fourth  imaginary 
dimension.  Because  time  and  the  three  space  co- 
ordinates are  thus  strictly  assimilated,  Lorentz's 
transformation  assumes  a  strictly  symmetrical  form. 
In  fact,  if  the  four  coordinates  are 

Xi  =  x,        Xi  =  y,         xz  =  z,         x  4=  ict 

where  i  denotes  V  —  1  and  c  the  velocity  of  light 
in  a  vacuum,  Lorentz's  transformation  becomes 


The  axes  being  at  right  angles,  the  coefficients 
Apq  satisfy  the  known  relations 

=  0,  when  q  ^  r; 

At       =     1. 


The  Lorentz  transformation  corresponds,  there- 
fore, to  a  displacement  of  the  reference  system  of 
four  axes  (translation  and  rotation  in  the  four-di- 
mensional space).  It  occurs  spontaneously  in  na- 
ture whenever  an  electromagnetic  system  is  moved 
by  a  translation  as  a  whole  with  respect  to  immov- 
able axes.  Hence  the  relativity  principle  may  be 
stated  as  follows  :  physical  laws  retain  the  same  form 
for  all  systems  of  rectangular  axes  in  four-dimensional 


RELATIVITY    PRINCIPLE  37 

space,  or  again,  if  we  call  these  systems  Lorentz 
systems :  systems  having  Lorentz  axes  are  equivalent. 

It  follows  as  a  result  of  the  structure  of  the  Lorentz 
group  that  the  concepts  of  space  and  time  cease  to 
be  independent  concepts;  they  are  absorbed  in  the 
more  general  concept  of  the  universe.  The  dura- 
tion of  phenomena  varies  according  as  it  is  measured 
by  observers  relatively  at  rest  or  in  motion.  For 
every  portion  of  matter  there  exists  a  local  time,  or 
time  proper,  which  is  the  interval  of  time,  measured 
by  observers  connected  with  the  system,  between . 
two  successive  events  in  it  which  for  them  coincide 
in  space. 

Simultaneity  loses  all  absolute  significance  and 
becomes  relative :  two  events  in  two  different  regions 
of  space  which  are  simultaneous  for  certain  observers 
cease  to  be  so  for  others  in  motion  with  respect  to 
the  former.  Even  the  order  of  succession  of  two 
events,  the  distance  between  which  in  space  exceeds 
the  path  traversed  by  light  during  their  interval, 
may  be  reversed  for  certain  groups  of  observers. 

These  new  ideas  of  space  and  time  lead  to  the 
erection  of  a  new  kinematics.  In  it  the  idea  of  a 
natural  Euclidean  solid  no  longer  exists,  since  all 
bodies  undergo  the  Lorentz  contraction  in  the  direc- 
tion of  their  translatory  motion.  If  we  still  desire 
to  talk  about  solids,  it  is  necessary  to  substitute 
for  Euclid's  geometry  that  due  to  Lobatschewsky : 
the  natural  solids  undergoing  the  Lorentz  con- 
traction behave  therefore  like  hyperbolic  solids  in 
a  space  of  negative  curvature,  taking  for  the 


38  PHILOSOPHY   AND    THE    NEW    PHYSICS 

value  of  the  space  constant  the  velocity  of  light 
V  =  3  X  1010  cm.  per  sec.1 

A  second  consequence  consists  in  the  impos- 
sibility of  observing  objects  moving  with  a  velocity 
exceeding  that  of  light.  This  follows  from  the 
Lorentz  contraction :  at  this  limiting  velocity  bodies 
would  become  infinitely  flattened  out  and  have  an 
infinite  inertia.  ,  This  may  be  derived  also  from 
the  constancy  of  the  velocity  of  propagation  of  light 
in  all  directions  for  any  observers  whatever  as 
follows  from  Michelson's  experiment.  It  follows 
from  this  experiment  that  a  luminous  ray  takes 
the  same  time  for  the  round  trip  OPO  when  it  is 
propagated  in  the  direction  of  the  translatory 
motion  of  the  earth,  so  that  its  velocity  is  combined 
with  the  velocity  of  that  motion,  and  when  it  is 
propagated  normally  or  obliquely  to  that  direction, 
a  fact  that  is  explained  by  the  existence  of  local 
time.  Therefore,  Galileo's  law  for  the  composition 
of  velocities  ceases  to  be  true:  two  velocities  v  and 
v'  in  the  same  sense  and  the  same  direction  may  not 
be  added  by  vector  addition  according  to  the  class- 
ical relation  v  +  vf,  but  must  be  added  according 
to  the  new  formula  (v  +  v')  /  (1  +  w'),*  where  the 
unit^of  velocity  is  taken  as  the  velocity  of  light: 
V  =  1.  All  instantaneous  action-at-a-distance  be- 
comes thereby  impossible. 

It  is  just  this  impossibility  of  any  instantaneous 

1  L.  Rougier,  De  1'utilisation  des  ge'ome'tries  non-euclidiennes 
dans  la  physique  de  la  relativite"  (L'Enseignement  mathe'matique, 
15  Janvier  1914,  p.  5-18). 

2  This  expression  is  always  less  than  1.     (Tr.) 


RELATIVITY    PRINCIPLE  39 

action-at-a-distance  that  leads  to  momentum,  and 
hence  mass,  being  attributed  to  radiant  energy, 
if  it  is  desired  to  preserve  Newton's  principle  of 
the  simultaneous  equality  of  action  and  reaction  or 
the  principle  of  conservation  of  the  total  momentum 
in  the  case  of  a  closed  system. 

Classical  mechanics  is  in  no  better  accord  with 
the  relativity  principle  than  Galilean  kinematics. 
There  is  an  incompatibility  between  the  Galileo 
group  that  conserves  without  change  the  form  of 
Lagrange's  canonical  equations,  and  the  Lorentz 
group  that  conserves  the  form  of  Maxwell's  equa- 
tions of  the  electromagnetic  field.  In  order  to 
put  them  into  accord  the  coefficient  of  Lorentz 


must  be  introduced  in  all  the  equations  of  dynamics. 

It  follows  from  this  that  all  forces  of  nature 
must  behave,  on  passing  from  one  reference  system 
to  another,  as  if  they  were  of  electromagnetic 
origin. 

In  what  follows  we  shall  retain  the  following 
consequences  of  the  relativity  principle  : 

1.  The    existence    of    absolute    motion    has    no 
physical  meaning. 

2.  All    bodies    contract    in    the    sense    of    their 
translatory  motion  in  the  ratio  \/l  —  /32. 

3.  No  velocity  exceeding  the  limiting  velocity 
of  light  in  a  vacuum  can  be  observed;  consequently, 
there  is  no  instantaneous  action-at-a-distance. 

4.  All  forces  behave  as  if  they  were  of  electro- 
magnetic origin. 


40  PHILOSOPHY    AND    THE    NEW    PHYSICS 

We  shall  retain  one  last  consequence.  The 
incompatibility  of  the  Lorentz  group  and  the  Galileo 
group  shows  the  futility  of  attempts  starting  from 
the  equations  of  Lagrange  and  Hamilton  to  explain 
mechanically  the  phenomena  of  nature,  and  in 
particular  electric  and  magnetic  phenomena. 

On  the  contrary,  what  must  be  done  is  to  reduce 
Lagrange's  equations  of  mechanics,  equations  that 
are  correct  as  a  first  approximation  for  low  veloc- 
ities, to  Maxwell's  equations  of  electromagnetism ; 
the  problem  is  to  explain  mechanical  phenomena 
on  tbe  basis  of  electric  phenomena. 


CHAPTER  III 
ELECTROMAGNETIC  DYNAMICS 

8.    THE      LOCALIZATION      OF      ENERGY      OUTSIDE      OF 
MATTER. 

The  considerations  that  have  led  physicists  to 
the  idea  of  the  inertia  of  'energy  are  derived  from 
Faraday's  and  Mosotti's  views  on  the  localization 
of  electric  energy  outside  of  conductors  in  the 
dielectric  space  surrounding  them. 

It  is  known  that  the  electrification  of  a  body 
determines  the  appearance  of  attracting  and  re- 
pelling forces  in  the  surrounding  space,  under  the 
influence  of  which  oppositely  electrified  bodies 
approach  each  other  and  similarly  electrified  bodies 
repel  each  other  in  accordance  with  Coulomb's  law. 
Before  Faraday,  the  appearance  of  these  forces  was 
explained  by  the  statement  that  there  exist  two 
imponderable  fluids,  vitreous  (positive)  electricity 
and  resinous  (negative)  electricity,  to  be  found  in 
the  interior  of  electrified  conductors,  the  quanti- 
ties of  which  constitute  the  charges  of  these  con- 
ductors. These  fluids  have  the  property  of  acting 
instantaneously  on  each  other  at  a  distance  and  this 
explains  the  electrostatic  actions.  The  region  of 
space  in  which  a  small  electrified  body  may  be 
directly  influenced  by  the  presence  of  electric  fluid, 

41 


42  PHILOSOPHY    AND    THE    NEW    PHYSICS 

distributed  inside  of  a  neighboring  conductor,  is 
called  the  electric  field  of  this  conductor.  The 
field  is  determined  at  every  point  of  space  by 
the  magnitude,  the  direction  and  the  sense1  of  the 
attracting  or  repelling  force  that  would  be  exerted 
on  an  electrified  body  brought  there. 

It  is  possible  to  draw  through  each  point  of  an 
electric  field  a  curve  whose  direction  coincides 
with  that  of  the  force  capable  of  thus  acting  at 
that  point:  an  infinite  set  of  lines  called  lines  of 
electric  force  is  thus  obtained.  These  lines  have  a 
purely  geometric  significance  :  that  is,  the  attracting 
and  repelling  forces,  the  direction  of  which  they 
symbolize,  do  not  exist  unless  an  electrified  body 
is  actually  brought  to  one  of  the  points  through 
which  they  pass.  In  this  case  only  do  they  acquire 
a  physical  significance  and  that  merely  at  the 
points  considered.  The  intensity  of  the  electric 
field  of  a  conductor  at  a  point  is  defined  in  magni- 
tude, sense  and  direction,  by  the  magnitude,  sense 
and  direction  of  the  force  that  acts  at  this  point  on 
the  unit  of  electric  mass  conventionally  chosen. 
If  we  call  /  the  force  exerted  on  the  unit  mass  of 
electricity  77,  the  intensity  of  the  field  is  represented 
by  the  relation 


1A  force  acts  in  a  certain  line  (direction)  and  in  a  certain  sense 
(i.e.,  either  forward  or  backward)  along  the  line.  In  works 
written  in  English  the  word  direction  usually  includes  both  ideas. 
(Tr.) 


ENERGY    OUTSIDE    OF   MATTER  43 

This  idea,  which  was  the  current  one  before  Fara- 
day, rests  on  three  postulates:  (1)  there  exist  im- 
ponderable fluids  (the  positive  electric  fluid,  the 
negative  electric  fluid,  the  positive  magnetic  fluid, 
the  negative  magnetic  fluid  and  the  caloric  fluid) 
the  presence  of  which  in  a  body  neither  increases 
nor  decreases  its  mass;  (2)  these  fluids  are  distrib- 
uted in  the  interior  of  bodies;  (3)  instantaneous 
action  at  a  distance  is  possible. 

Faraday  rejects  these  postulates.  By  means  of 
celebrated  experiments  he  establishes  the  fact  that 
the  electric  field  is  zero  in  the  interior  of  conductors, 
that  is,  that  their  charge  does  not  manifest  itself 
except  at  their  surface  and  in  the  surrounding  space. 
He  rejects  the  idea  of  instantaneous  action-at-a- 
distance  and  considers  the  lines  of  force  as  having  a 
real  physical  significance;  they  correspond,  according 
to  him,  to  certain  permanent  modifications  of  a 
dielectric  medium,  called  the  ether,  filling  all  space 
and  existing  between  the  conductors.  The  mechan- 
ical state  of  this  medium  around  an  electrified  body 
is  what  determines  the  forces  to  which  this  body  is 
subject;  and  the  electric  charge  carried  by  a  con- 
ductor is  determined  by  the  number  of  lines  or  tubes 
of  force  attached  to  it.  Starting  from  the  concept  of 
forces  propagated  by  contact  from  point  to  point 
with  the  velocity  of  light,  Maxwell  has  accounted 
for  the  electrostatic  actions,  in  conformity  with 
Faraday's  views  and  in  accord  with  his  experiments. 

It  is  possible  to  get  rid  of  the  consideration  of  the 
ether,  the  existence  of  which  is  hypothetical,  and, 


44  PHILOSOPHY    AND    THE    NEW    PHYSICS 

as  we  shall  see,  contradictory,  and  contemplate 
nothing  but  the  only  positively  accessible  reality: 
electrostatic  energy  localized  outside  of  the  con- 
ductors in  the  form  of  the  field.  The  mechanical 
work  of  attraction  or  repulsion,  done  by  the  static 
forces  appearing  in  an  electric  field,  represents  a  cer- 
tain expenditure  of  energy,  that  is,  the  change  of 
a  certain  amount  of  potential  energy  into  actual 
energy  of  motion.  Thus  potential  energy  localized 
in  empty  space  around  a  conductor  exists  in  con- 
formity with  Faraday's  experiments.  This  elec- 
trostatic potential  energy  comes,  by  virtue  of  the 
principle  of  the  conservation  of  energy,  from  the 
work  expended  in  producing  the  state  of  electrifica- 
tion of  the  conductor.  The  energy  per  unit  volume 
is  proportional  to  the  square  of  the  intensity  of  the 
corresponding  field.  Let  dr  be  a  volume  element 
taken  in  this  space  and  let  h  be  the  vector  defining 
in  magnitude,  sense  and  direction  the  intensity  of 
the  field  at  a  point  A  of  this  element ;  then  the  density 
of  the  energy  localized  in  the  volume  dr  has  the  value 


where  KQ  represents  the  specific  inductive  capacity 
of  space,  the  numerical  value  of  which  depends  on 
the  choice  of  units.  To  find  the  energy  localized 
in  a  portion  of  space  of  finite  extent  it  is  sufficient 
to  calculate  the  integral 

We    = 

in  this  space. 


ENERGY    OUTSIDE    OF   MATTER  45 

Thus,  for  the  empty  space  surrounding  a  con- 
ductor, Faraday's  experiments  and  the  principle  of 
the  conservation  of  energy  lead  to  the  assumption 
of  the  localisation  of  a  certain  amount  of  electric  energy 
outside  of  matter. 

The  same  considerations  may  be  applied  to  a 
magnetic  field  produced  by  a  magnet  or  a  current. 
Similarly  the  energy  localized  in  a  region  of  empty 
space  is  equal  to  the  integral 


W.  =     I  ri"-  dr, 

J          ^^ 

where  H  denotes  the  vector  defining  the  intensity  of 
the  field  at  a  point  A  of  the  volume  element  dr  and 
MO  the  permeability  of  empty  space. 

The  same  conclusions  are  reached  by  consider- 
ing radiation  freely  propagated  in  empty  space  with 
the  velocity  of  light. 

This  radiation,  if  taken  at  a  sufficiently  large 
distance  from  its  source,  may  be  regarded  as  formed 
by  the  superposition  of  an  electric  and  a  magnetic 
field,  one  at  right  angles  to  the  other  and  both 
normal  to  the  direction  of  propagation. 

This  electromagnetic  field  represents  a  cer- 
tain amount  of  energy  outside  of  any  material  sub- 
stratum, the  energy  density  of  which  in  every  unit 

Tf  h  2  IT  2 

volume  that  it  occupies  is  equal  to  -      -  +  ^  — , 

O7T  O7I 

the  electric  energy  being  equal  to  the  magnetic  en- 
ergy in  every  freely  propagated  plane  wave,  so  as  to 
give  the  relation 


46  PHILOSOPHY    AND    THE    NEW    PHYSICS 

The  localisation  of  electromagnetic  energy  of  free 
radiation  in  empty  space  follows  from  the  principle 
of  the  conservation  of  energy,  as.  may  be  readily 
demonstrated.  Let  us  consider  a  material  source 
radiating  energy  in  a  definite  direction  and  an 
obstacle  absorbing  it  completely.  At  start  there 
is  a  loss  of  energy  of  the  source  and  on  arrival 
a  recovery  of  this  energy  by  the  obstacle.  The 
velocity  of  propagation  of  radiation  being  finite 
because  equal  to  that  of  light,  we  would  not  have 
conservation  of  energy  at  every  instant  between  the 
time  of  emission  and  that  of  absorption,  unless  ra- 
diation represented  a  transfer  of  energy  through 
empty  space  proportional  to  the  energy  radiated  at 
the  start  and  absorbed  on  arrival. 

Thus  the  principle  of  the  conservation  of  energy 
and  Faraday's  experiments  lead  us  to  assume 
the  localisation  of  electric  and  magnetic  energy 
in  empty  space,  outside  of  matter,  around  charged 
conductors  and  natural  or  artificial  magnets.  Nev- 
ertheless electrostatic  potential  energy  is,  in  the 
case  of  a  charged  conductor,  still  closely  bound 
to  matter,  for  the  vector  representation  of  the  elec- 
trostatic field  shows  the  lines  or  tubes  of  force  to 
be  attached  to  the  surface  of  a  conductor  and  to 
spread  radially  roundabout.  In  the  case  of  an  arti- 
ficial magnet  formed  by  the  magnetic  field  produced 
by  a  current  flowing  in  a  metallic  circuit,  the  mag- 
netic lines  of  force  do  not  abut  on  the  circuit: 
they  embrace  it  by  returning  on  themselves;  but 
they  still  proclaim  its  immediate  neighborhood. 


ELECTROMAGNETIC    INERTIA  47 

This  is  no  longer  so  in  the  case  of  radiant  energy, 
which  manifests  itself  to  our  senses  sometimes  as 
light,  sometimes  as  heat,  sometimes  in  the  shape  of 
Hertzian  waves.  Radiation  represents  a  localisa- 
tion, in  empty  space,  of  electromagnetic  energy  that 
is  independent  of  the  immediate  neighborhood  of 
any  matter,  and  is  capable  of  being  propagated 
indefinitely  in  a  given  direction  without  ever  meet- 
ing bodies  which  absorb  it.  Hence  the  first  pos- 
tulate of  the  dualistic  theory  must  be  rejected, 
namely  that  energy  can  not  be  localized  outside  of 
matter. 

9.    ELECTROMAGNETIC    INERTIA   AND    THE    DYNAMICS 
OF  AN  ELECTRIFIED  PARTICLE  IN  MOTION. 

If  the  first  postulate  of  the  dualistic  doctrine 
has  been  set  at  nought  as  a  consequence  of  Faraday's 
experiments,  its  second  postulate  has,  since  1881, 
been  shaken  as  a  consequence  of  the  theoretical 
researches  of  J.  J.  Thomson.1  This  young  physicist 
had  the  merit  of  being  the  first  one  to  understand 
that  an  electrified  body  possesses,  because  of  the 
electrostatic  energy  of  its  charge,  a  supplementary 
inertia  of  electromagnetic  origin.  This  results  from 
the  self-induction  of  conduction  currents;  from  the 
existence  of  convection  currents  as  a  consequence 
both  of  the  laws  of  Maxwell  and  Hertz  of  the 
electromagnetic  field  and  Rowland's  experiments 
relating  to  an  electrified  body  in  motion;  and  lastly 

1  J.  J.  Thomson,  Philosophical  Magazine,  5  ser.  vol.  xi,  1887, 
p.  219. 


48  PHILOSOPHY    AND    THE    NEW    PHYSICS 

from  the  identity,  as  regards  magnetic  actions,  of 
conduction  and  convection  currents. 

When  the  intensity  of  a  current  changes,  a 
counter-electromotive  force  is  produced  in  the  cir- 
cuit and  this,  in  accordance  with  Lenz's  law,  tends 
to  oppose  the  change  of  the  current.  This  is  self- 
induction  which  is  a  veritable  electric  inertia:  it 
opposes  the  change  in  intensity  of  a  current,  just  as 
inertia  of  matter  opposes  a  change  in  velocity  of 
moving  bodies.  Just  as  a  certain  effort  must  be 
expended  to  put  a  body  in  motion,  a  certain  work 
must  be  expended  to  establish  a  current ;  and  again, 
just  as  a  projected  body  tends  to  conserve  its  ve- 
locity, so  does  a  current  once  established  tend  to 
maintain  its  intensity.  If  a  current  increases  or 
decreases  under  the  action  of  an  external  field,  a 
counter-electromotive  force  is  produced  which  op- 
poses the  change  of  the  current,  just  as  the  inertia 
force  of  a  moving  body  that  is  accelerated  or  re- 
tarded opposes  the  external  actions  that  produce 
this  change. 

The  existence  of  convection  currents  was  fore- 
seen theoretically  by  Maxwell  and  was  verified  by 
experiment  by  Rowland  and  his  pupils.1  It 
results  from  the  laws  established  by  Maxwell  and 
Hertz  as  to  the  interdependence  which,  in  time  and 
space,  connects  the  change  of  the  two  fields,  the 
electric  and  magnetic.  They  may  be  summarized 
qualitatively  as  follows:  any  change  in  one  of  the 

1  Cre'mieu,  Etat  actuel  de  la  convection  e"lectrique  (Bulletin  des 
stances  de  la  Socie"te"  frangaise  de  Physique,  1902,  3  fasc.,  p.  155). 


ELECTROMAGNETIC    INERTIA  49 

two  fields  at  a  point  in  space  as  time  goes  on,  gives 
rise  to  the  other  field,  the  field  thus  created  being 
distributed  in  lines  of  force  which  encircle  the  direction 
in  which  the  first  field  changes.  A  change  in  the 
magnetic  field  in  a  given  region  of  space  produces 
an  electric  field,  the  lines  of  force  of  which  encircle 
the  direction  in  which  the  magnetic  field  changes: 
this  is  the  phenomenon  of  static  induction  dis- 
covered by  Faraday.  If  the  space  where  this 
field  is  thus  created  happens  to  be  occupied  by  a 
conductor,  currents  that  encircle  the  direction  in 
which  the  magnetic  field  changes  are  induced  in  it. 
Inversely,  a  change  of  the  electric  field  in  a  given 
region  of  space  produces  a  magnetic  field,  the  lines 
of  force  of  which  encircle  the  direction  in  which  the 
electric  field  changes;  this  is  the  convection  current 
foreseen  by  Maxwell  and  brought  to  light  by 
Rowland's  celebrated  experiment. 

Let  us  consider,  according  to  this  law,  a  point  A 
taken  in  the  electrostatic  field  of  an  electrified 
particle  that  is  being  displaced  carrying  its  charge 
along  with  it.  The  intensity  at  A  changes  because 
the  particle  approaches  this  point,  passes  it,  and 
moves  away.  There  is  a  variation  of  the  electric 
field  in  a  fixed  region  of  space  as  time  goes  on; 
therefore  a  magnetic  field  is  produced  on  account  of 
the  law  of  the  convection  current.  Hence  an  elec- 
trified particle  in  motion  behaves  like  an  element 
of  a  voltaic  current;  to  put  it  more  exactly,  the 
charge  e  that  it  carries  with  a  velocity  v  is  equiva- 
lent, as  regards  magnetic  actions  exerted  by  it,  to  an 


50  PHILOSOPHY    AND    THE    NEW    PHYSICS 

element  of  voltaic  current  having  the  intensity  i 
and  the  length  dl,  so  that  idl  =  ev.  The  name 
convection  current  is  given  to  the  current  thus 
produced. 

Let  us  now  consider  an  electrified  sphere  of 
radius  a  having  a  surface  charge  e.  At  rest  it  is 
surrounded  by  radial  lines  of  force,  distributed 
symmetrically  all  around,  which  correspond  to  a 
localization  of  electrostatic  energy  equal  to  the 
work  that  had  to  be  expended  to  produce  the  state 
of  electrification  of  the  sphere,  and  which  has  the 
value 

(2)  *•-&* 

If  a  rectilinear  uniform  motion  with  a  velocity 
v,  small  compared  with  that  of  light,  be  communi- 
cated to  this  sphere,  it  carries  along  its  train  of  lines 
of  force,  radially  and  symmetrically  distributed 
as  when  at  rest.  On  account  of  the  variation, 
as  a  function  of  the  time,  of  the  electric  field  at 
a  point  A  of  space,  it  produces  a  magnetic  field 
distributed  in  circular  lines  of  force  encircling  the 
direction  of  motion.  The  field  at  the  point  A  in 
a  direction  perpendicular  to  the  plane  passing 
through  A  itself,  the  instantaneous  position  0  of  the 
particle,  and  the  direction  of  the  velocity  has  the 
value 

ev  sin  a 
=        r2 

where  a  denotes  the  angle  A  Ov  and  r  the  distance 
AO.  The  field  thus  produced,  which  varies  inversely 


ELECTROMAGNETIC    INERTIA  51 

as  the  square  of  the  distance,  is  determined  by  the 
instantaneous  position  of  the  sphere.  The  latter 
carries  along  in  its  motion  the  system  of  circular 
magnetic  lines  of  force  superimposed  on  the  radial 
electric  lines  of  force.  This  system  of  lines  of 
force  constitutes  the  electromagnetic  field  of  the 
moving  particle,  moving  with  it  like  the  wave  sys- 
tem following  a  ship.  It  remains  invariable  so 
long  as  the  velocity  remains  constant.  The  mag- 
netic field  thus  superimposed  on  the  electric  field 
represents  a  localization  of  energy,  equivalent  to 
the  work  expended  by  external  forces  in  communi- 
cating the  velocity  v  to  the  charged  sphere.  This 
energy  that  continues  bound  to"  it  in  its  motion 
would  be  recovered  when  it  is  arrested,  in  the  form  of 
work  done  against  the  retarding  actions.  An  easy 
calculation  based  on  the  expression  for  the  volume 

TJ2 

density  of  energy  -|—    shows  that  it  is  equal  to 

O7T 

(4)  *--£*. 

which  expression  may  be  put  into  the  more  sugges- 
tive form 

(40  *V- 


3a 

This  energy  presents  all  the  characteristics 
of  kinetic  energy  >^mz>2,  including  that  of  being 
proportional  to  the  square  of  the  velocity.  Every- 
thing takes  place  as  if,  contrary  to  the  second  pos- 
tulate of  the  dualistic  doctrine,  the  sphere  possessed, 
on  account  of  the  potential  energy  of  its  charge,  a 


52  PHILOSOPHY    AND    THE    NEW    PHYSICS 

supplementary  inertia,   an   additional   kinetic  mass 
of  electromagnetic  origin,  equal  to 

r*\  2»*e2 

(5)  m0  =  -p- 

This  is  a  necessary  consequence  of  the  iden- 
tity of  conduction  and  convection  currents.  The 
inertia  of  a  charged  particle  in  motion  is  due  to 
the  self-induction  of  the  convection  current  that 
it  produces;  since  electric  self-induction  has  the  same 
properties  as  the  inertia  'of  matter,  it  follows  that 
this  particle,  on  account  of  its  electrification,  has 
an  increment  of  its  capacity  for  kinetic  and,  conse- 
quently, electromagnetic  energy  which  becomes 
super-imposed  on  its  inertia  proper. 

Electromagnetic  inertia  due  to  the  presence 
of  a  charge  on  a  conductor  in  motion  is  proportional 
to  the  electrostatic  potential  energy  that  this 
charge  represents  and  that  the  sphere  carries  along 
with  itself.  Any  change  of  this  charge  or  of  the 
radius  of  the  sphere,  causing  a  change  of  the  poten- 
tial energy  stored  around  it,  must  imply  a  correlated 
change  of  this  inertia.  The  question  might  then 
be  raised,  what  would  happen  if  the  sphere  had  a 
velocity  approaching  that  of  light  and  its  motion 
remained  always  quasi-stationary,  that  is,  not  sub- 
ject to  any  appreciable  acceleration.  This  is  the 
theoretical  problem  that  has  been  conceived  by  Max 
Abraham. l 

In  order  to  solve  it  we  must  refer  to  Maxwell's 
law  on  the  mutual  dependence  of  the  electric  and 

1  Max  Abraham,  Annalen  der  Physik,  vol.  x,  1903,  p.  105-179. 


ELECTROMAGNETIC    INERTIA  53 

the  magnetic  fields.  The  magnetic  field  produced 
at  a  fixed  point  in  space  by  the  moving  particle 
changes  with  the  time,  according  as  the  particle 
approaches,  passes  and  recedes,  carrying  along  its 
train  of  lines  of  force.  This  change  of  the  mag- 
netic field  must,  in  accordance  with  Maxwell's  law, 
be  accompanied  by  the  production  of  an  induced 
electric  field  which  is  superimposed  on  the  electric 
field  given  by  Coulomb's  law  and  modifies  its  dis- 
tribution. The  analysis  of  the  phenomenon  shows 
that  the  electric  lines  of  force  tend  to  place  them- 
selves in  a  direction  transverse  to  that  of  the  motion, 
and  reach  this  state  completely  when  the  velocity 
reaches  that  of  light.  The  limiting  distribution  of 
the  field  thus  realized  represents  an  infinite  energy 
and  consequently  an  infinite  inertia;  so  that 
infinite  work,  requiring  an  infinite  time,  would  be 
necessary  to  bring  an  electrified  particle  to  a  perma- 
nent condition  in  which  it  would  have  the  velocity 
of  light.  This  velocity  appears  as  a  limit  that  no 
electrified  body  can  reach.  This  is  confirmed  by 
the  fact  that  the  velocity  of  cathode  particles 
reaches  nine-tenths  of  that  of  light  without  succeed- 
ing in  attaining  it;  this,  moreover,  leads  to  the 
kinematic  law  of  the  composition  of  velocities,  de- 
manded by  the  relativity  principle. 

The  modification  of  the  electric  field  in  con- 
sequence of  the  induced  field  superimposed  on 
it  carries  with  it  that  of  the  force  of  inertia  that 
the  particle  opposes  to  changes  of  velocity.  The 
electromagnetic  mass  ceases  to  be  proportional  to 


54  PHILOSOPHY   AND    THE    NEW    PHYSICS 

the  velocity  with  a  constant  coefficient;  it  varies 
with  the  velocity  according  to  a  certain  function, 
in  such  a  way  as  to  become  infinite  for  the  limiting 
velocity  of  light,  and  this  in  a  different  manner 
for  the  three  definitions  of  mass  and  according  to 
the  direction  of  the  acceleration  with  respect  to 
that  of  the  motion.  In  the  simplest  case,  that  of 
an  undeformable  spherical  body,  two  masses  must 
be  distinguished;  the  longitudinal  mass,  the  force 
divided  by  the  acceleration,  if  the  latter  is  tan- 
gential to  the  motion;  the  transverse  mass  if  the 
acceleration  is  normal  to  the  motion.  The  first 
case  corresponds  to  a  change  in  magnitude  of  the 
velocity  without  a  change  of  direction,  the  second 
to  a  change  in  direction  without  a  change  in  mag- 
nitude. We  may  call  the  value  of  m0,  which  for  low 
velocities  is  the  same  for  the  different  definitions  of 
mass,  initial  mass  mQ  and  reserve  the  name  electro- 
magnetic mass  m  for  the  transverse  mass.  This 
mass  m  is  identical  with  the  Maupertuisian  mass;  it 
is  the  only  one  accessible  to  the  measurements  on 
the  electric  and  magnetic  deviations  of  the  cathode 
particles  in  a  Crookes'  tube. 

To  find  what  function  connects  the  change 
of  mass  with  that  of  velocity,  the  shape  of  the  par- 
ticle and  the  distribution  of  its  charge  must  be 
specified.  Max  Abraham  considers  the  case  of  an 
undeformable  sphere  having  a  surface  charge  of  uni- 
form distribution:  for  the  different  definitions  of 
mass  he  arrives  at  rather  complicated  formula?, 
all  of  which  assign  the  velocity  of  light  as  the  upper 


ELECTROMAGNETIC    INERTIA  55 

limit  of  the  velocity  of  electrified  bodies.  Lorentz,1 
however,  in  order  to  account  for  the  negative 
result  of  the  experiments  to  discover  the  abso- 
lute motion  of  the  earth,  was  led  to  assume  the 
contraction  of  all  bodies  in  the  direction  of  their 


translatory  motion  in  the  ratio  \/l  —  02  f°r  ob- 
servers who  see  them  pass.  A  moving  sphere  be- 
comes a  flattened  ellipsoid.  Allowing  for  this 
deformation,  which  modifies  the  distribution  of  the 
electric  lines  of  force  at  the  surface  of  a  charged 
sphere  and,  consequently,  the  intensity  of  the  con- 
vection current  produced  by  it  and  the  laws  of  the 
variation  of  the  self-induction  of  the  current  as 
function  of  the  velocity,  Lorentz  has  obtained  a 
formula  much  simpler  than  that  of  Abraham  for 
the  Maupertuisian  mass  or  the  transverse  mass, 
which  becomes  equal  to 

/  r>\  ^0 

(6)  ra  =      . 

V1-/32 

By  starting  from  this  formula  the  laws  of  varia- 
tion corresponding  to  the  other  definitions  of  mass 
are  readily  obtained. 

The  fortunate  parallelism,  which  existed  at  that 
time  between  the  progress  of  theoretical  physics 
and  the  discoveries  of  experimental  physics,  re- 
vealed in  the  cathode  particles  of  Crookes'  tubes, 
later  in  the  0  rays  issuing  from  the  atomic  dis- 
integration of  radioactive  bodies,  electrified  bodies 

1  H.  A.  Lorentz,  Versuch  einer  Theorie  der  elektrischen  und 
optischen  Erscheinungen  in  bewegten  Korpern,  Leyden,  1895. 


56  PHILOSOPHY   AND    THE    NEW    PHYSICS 

projected  with  velocities  close  to  that  of  light. 
It  became  possible  to  test  whether  their  inertia 
varied  with  the  velocity,  according  to  the  theoretical 
anticipation  of  Max  Abraham,  or  according  to  that 
of  Lorentz,  and  to  distinguish  between  the  formulae 
proposed  by  these  two  authors. 

The  experiments  of  Kaufmann  showed  that  the 
mass  actually  varies  with  the  velocity  according  to 
the  formula  of  Abraham;  but  the  more  recent  ex- 
periments of  Bucherer  and  of  Hupka,  of  a  higher 
degree  of  precision,  showed  that  the  change  of  the 
electromagnetic  mass  of  0  corpuscles  is  better 
represented  by  the  formula  of  Lorentz.  We  shall 
see  that  the  relativity  principle  leads  to  an  extension 
of  this  formula  to  all  kinds  of  moving  bodies,  whe- 
ther electrified  or  not,  so  that  they  behave  as  if  their 
inertia  was  solely  of  electromagnetic  origin.  It 
follows  from  this  that,  contrary  to  the  third  postu- 
late of  the  dualistic  theory,  the  mass  of  bodies  is 
not  an  invariable  scalar  quantity,  independent  of 
their  state  of  motion  or  of  rest.  It  is  a  quantity  having 
the  symmetry  of  a  tensor,1  and  dissymmetrical  and 
variable  as  a  function  of  the  velocity. 

JIn  modern  applications  of  vector  analysis,  the  branch  of 
mathematics  dealing  with  the  algebra  and  calculus  of  directed 
quantities  or  vectors,  the  concept  of  tensor  plays  an  important 
part.  A  symmetrical  tensor  is  an  aggregate  of  9  quantities, 
which,  when  combined  with  the  3  components  of  a  vector  by  3 
symmetrical  relations,  give  the  3  components  of  a  new  vector.  A 
non-symmetrical  tensor  is  more  complicated.  Earlier  writers 
attached  a  quite  different  meaning  to  the  word  tensor;  it  was 
used  by  them  to  denote  the  mere  magnitude  of  a  single  vector. 
(Tr.) 


CHAPTER  IV 
THE  ELECTRONIC  THEORY  OF  MATTER 

10.    LORENTZ'S  SYNTHESIS. 

The  interest  of  Kaufmann's  and  Bucherer's 
experiments  is,  however,  not  limited  to  the  fore- 
going result.  By  subjecting  cathode  particles 
to  the  action  of  an  electric  field  and  a  magnetic 
field  the  comparison  of  the  two  deviations  thus  pro- 
duced permits  of  finding  the  velocity  of  these 
particles  and  the  ratio  e/m  of  their  charge  to  their 
mass.  If  their  charge  is  held  to  be  constant  and 
to  be  the  same,  these  experiments  then  reveal  the 
variation,  as  a  function  of  the  velocity,  of  the  total 
apparent  mass  of  these  particles,  consisting  of  the 
sum  of  their  material  mass  and  their  electromagnetic 
mass.  Comparing,  then,  the  law  of  the  total  mass,  as 
derived  from  the  preceding  experiments  with  the 
law  of  variation  of  the  electromagnetic  mass,  theo- 
retically calculated,  the  ratio  of  the  material  mass 
to  the  total  apparent  mass  may  be  deduced.  The 
result  obtained  is  remarkable:  the  inertia  of  cathode 
particles  is  solely  of  electromagnetic  origin.  These 
particles  constitute  elementary  electric  charges  with- 
out material  support,  atoms  of  negative  electricity 
called  electrons.  Thus  we  have  here,  contrary  to 
the  dualistic  theory,  a  form  of  energy,  resinous 

57 


58  PHILOSOPHY   AND    THE    NEW    PHYSICS 

(negative)  electricity,  that  appears  to  be  endowed 
with  inertia  and  corpuscular  structure  without  any 
material  substratum. 

This  result  was  the  starting-point  of  the  electronic 
theory  of  matter.1  It  consists  in  a  change  of  every- 
thing for  its  opposite,  a  reversal  of  the  relation  tra- 
ditionally supposed  to  exist  between  matter  and 
electricity.  In  place  of  seeking  to  explain  electric 
phenomena  mechanically,  the  mechanical  pheno- 
mena are  now  to  be  explained  electrically.  Instead 
of  seeking,  as  Maxwell  did,  to  cast  the  equations 
of  the  electromagnetic  field  in  the  analytical 
mould  made  by  Lagrange  and  Hamilton,  which 
appears  no  longer  valid  except  as  a  first  approx- 
imation for  low  velocities  and  for  quasi-stationary 
motions,  there  is  substituted  for  the  dynamics  of 
the  material  point,  conforming  to  Newton's  equa- 
tions, the  dynamics  of  the  electron,  conforming  to 
Lorentz's  equations.2 

Matter,  the  substratum  of  mechanical  phenome- 
na, is  explained  by  starting  from  electricity.  The 
elementary  charges  of  electrolytic  ions,  the  cath- 
ode particles  issuing  from  Crookes'  tubes,  the 
|8  rays  issuing  from  the  atomic  disintegration  of 
radioactive  bodies,  the  negative  emissions  consti- 
tuting the  Edison  and  the  Hertz  phenomena  reveal 
a  universal  constituent  of  matter  in  the  electron. 

1  Cf.  Les  ide"es  modernes  sur  la  constitution  de  la  matiere,  Con- 
ferences faites  en  1912  &  la  Societe"  francaise  de  Physique.     Paris, 
1913. 

2  Cf.  W.  Wien,  Archives  ne"erlandaises,  2.  ser.  vol.  V,  p.  96. 


LORENTZ'S   SYNTHESIS  59 

The  molecular  structures  constituting  ponderable 
bodies  are  nothing  but  electronic  architecture. 
Electrons  are  grains  of  resinous  (negative)  elec- 
tricity, all  identical  with  one  another.  They  carry 
an  individual  charge  of  4.774  X  10~10  electrostatic 
C.  G.  S.  units,  distributed  on  a  circumference  of  2 
millionths  of  a  MM  (2  X  10~12  millimeter)  radius. 
They  are  endowed  with  an  initial  electromagnetic 
mass  equal  to  10~17  grams,  that  is,  1800  times  smaller 
than  that  of  a  hydrogen  atom.  They  play  different 
parts  in  the  production  of  phenomena,  according  to 
the  position  that  they  occupy  in  the  atomic  and 
molecular  structures  and  according  to  the  degrees  of 
freedom  that  they  enjoy  because  of  this  position. 
Accordingly  there  are  distinguished:  perfectly  free 
electrons  moving  outside  of  matter,  in  the  form  of 
cathode  rays  and  0  rays;  free  electrons  moving  inside 
of  matter  in  the  intermolecular  spaces  with  a  chaotic 
motion  that  gives  rise  to  heat  radiation,  on  which 
may  be  superimposed  a  translatory  motion  as  a 
whole  that  gives  rise  to  electric  current  in  conduc- 
tors; electrons  weakly  bound  to  atoms  revolving  on 
their  circumference  and  capable  of  being  detached 
easily  under  the  action  of  shock  or  an  electromagne- 
tic action,  producing  thereafter  ionization  of  solu- 
tions and  gases;  electrons  bound  to  atoms,  moving  in 
closed  curves,  and  determining  the  spectral  rays  as 
well  as  the  chemical  valences,  the  sources  of  molecu- 
lar union;  lastly,  the  electrons  that  compose  the 
central  kernel  of  the  atom,  inaccessible  to  external 
physical  agents,  in  a  chaotic  state  of  agitation, 


60  PHILOSOPHY    AND    THE    NEW    PHYSICS 

which  do  not  become  revealed  except  in  the  atomic 
disintegration  of  radioactive  bodies. 

On  this  view  the  atoms  are  formed  by  negative 
electrons,  bound  more  or  less  to  the  kernel,  and  of 
positive  remainders,  the  charge  of  which  must  be 
equivalent  to  the  total  charge  of  the  negative  elec- 
trons in  order  to  maintain  in  the  neutral  state  the 
cohesion  of  the  structure  by  the  mutual  attraction 
of  the  electricities  of  opposite  kind.     Of  the  struc- 
ture of  these  positive  charges  we  know  next  to 
nothing.     Those  that  we  can  capture  in  the  canal 
rays   of  Goldstein  and  the  a  rays  of  radioactive 
bodies  are  atoms  of  hydrogen  or  helium,  deprived  of 
one  or  more  negative  electrons  and  having,  on  that 
account,  become  positive  ions.     It  may   be  asked 
whether  there  is  a  vitreous  (positive)   electricity, 
having  an  independent  existence  and  a  corpuscular 
structure  like  the  resinous  (negative)  electricity,  so 
that  there  would  be  positive  electrons  side  by  side 
with  the  negative  ones,  as  Jean  Becquerel  believes 
can  be  inferred  from  the  study  of  absorption  spectra 
at  low  temperatures;  or  whether  positive  electrifica- 
tion results  from  the  subtraction  of  one  or  more 
negative  electrons  from  the  normal  atomic  structure 
corresponding  to  the  neutral  state.     In  any  case 
the  question  of  finding  whether  positive  electricity 
has  a  material  support,  so  that  there  would  be  nega- 
tive electrons  but  only  ions  of  positive  charge,  has 
lost   much   of   its  interest.     The   relativity   prin- 
ciple leads,  as  Lorentz  has  shown,  to  the  assumption 
that  the  inertia  of  these  positive  ions,  if  they  can 


LORENTZ'S    SYNTHESIS  61 

not  be  decomposed  into  simpler  units,  must  follow 
the  same  laws  of  change  as  a  function  of  the  veloc- 
ity as  that  of  the  negative  electrons,  that  is,  that 
these  ions  must  behave  as  if  their  mass  were  solely 
of  electromagnetic  origin. 

The  electronic  theory  has  explained,  with  in- 
creasing success — which  has  only  reached  its  limit 
when  confronted  by  black  radiation  and  the  diminu- 
tion of  the  specific  heats  at  low  temperatures — the 
phenomena  of  static  electricity,  of  the  electr  c 
current,  of  induction  and  magnetism,  of  the  emis- 
sion, the  propagation  in  different  physical  media, 
and  the  absorption  of  different  kinds  of  radiation; 
those  of  radioactivity,  of  the  ionization  of  gases  and 
liquids,  of  chemical  valence,  etc.  It  has  led  to 
the  explanation  of  new  phenomena  such  as  the  phe- 
nomena of  Edison  and  of  Hertz,  and  above  all  the 
Zeeman  effect.  It  has  led  Lorentz1  to  a  brilliant 
synthesis  carrying  his  name.  Presented  for  the 
first  time  in  1892,  this  synthesis  has  been  put  into 
accord  with  the  requirements  of  the  relativity  prin- 
ciple by  its  author.  According  to  it  there  is  no 
matter,  only  electrons,  positive  and  negative,  in 
an  ocean  of  uniform  ether;  all  forces  are  of  elec- 
tromagnetic origin  or  behave  like  such;  and  the 
measurements  effected  in  a  moving  system  are  rela- 
tive to  the  dimensions  of  the  instruments,  to  the 
forces  taken  as  comparison  terms,  and  to  local  time. 

1  Cf.  H.  A.  Lorentz,  Sur  la  theorie  des  electrons  (Les  quantity's 
elementaires  d'61ectricite,  ions,  electrons,  corpuscules,  Paris,  1905, 
vol.  i,  p.  430-476). 


62  PHILOSOPHY    AND    THE    NEW    PHYSICS 

In  this  conception  matter,  conduction  currents  and 
magnetism  become  mere  modes  of  manifestation. 
The  only  constitutive  principles  are  the  ether  and 
grains  of  vitreous  (positive)  and  resinous  (negative) 
electricity.  We  shall  see  how  the  English  physi- 
cists have  taken  hold  of  this  conception  and  pushed 
the  reduction  in  the  number  of  things  still  further: 
according  to  certain  of  them  not  only  is  the  exist- 
ence of  matter  denied  but  also  that  of  electricity; 
and  nothing  but  ether  and  empty  space  exists. 

11.    THE  DEMATERIALIZATION  OF  MATTER. 

The  conception  of  the  dematerialization  of  matter 
of  the  English  physicists  results  from  the  success 
of  the  electronic  theory,  taken  in  connection  with 
the  concept  of  an  ether  endowed  with  mechanical 
properties,  that  is,  inertia,  elasticity  and  rigidity, 
in  conformity  with  the  ideas  of  Faraday  and 
Maxwell.  * 

It  is  the  wave  theory  of  light,  stated  at  first 
by  Leonardo  da  Vinci  and  Galileo,  made  more  pre- 
cise by  Huygens  following  the  discoveries  of  Grim- 
aldi,  and  established  finally  by  Fresnel  following 
Foucault's  experiment  that  has  given  physical 
verisimilitude  to  the  idea  of  an  ether.  If  light  and, 
in  general,  any  form  of  radiant  energy  is  a  wave 
phenomenon  that  is  propagated  with  a  finite 
velocity  in  the  interstellar  spaces,  it  is  difficult 
to  avoid  the  assumption  that,  because  there  is  wave 
vibration  and  therefore  motion,  there  is  something 
that  moves,  a  mobile  medium  that  must  fill  all 


DEMATERIALIZATION    OF   MATTER  63 

space.  As  Lord  Salisbury  picturesquely  said  in  his 
Oxford  presidential  address  to  the  British  Associa- 
tion, the  first  and  principal  reason  for  the  existence 
of  the  ether  is  to  supply  a  subject  to  the  verb  to 
undulate. 

The  second  object  of  the  ether  is  to  account  for 
the  localization  of  energy  in  dielectrics,  surrounding 
conductors  or  magnets,  in  accordance  with  Fara- 
day's experiments,  and  for  its  accumulation  in 
the  neighborhood  of  a  moving  electric  charge,  in 
accordance  with  the  theoretical  views  of  Abraham 
and  Lorentz  and  the  experimental  confirmations  of 
Kaufmann  and  Bucherer.  This  energy,  considered 
as  a  mode  of  manifestation  of  a  substance,  requires 
a  substratum  of  which  it  is  merely  an  accident. 
Lastly,  actions  at  a  distance,  such  as  gravitational 
attraction,  electric  or  magnetic  attraction  and  re- 
pulsion,rand,without  doubt,  chemical  affinity,  be- 
tween bodies  separated  in  space  are  incapable  of 
mental  representation  except  as  pressures  or  ten- 
sions exerted  by  an  intermediate  medium  in  which 
the  bodies  are  immersed.  To  account  for  the  phe- 
nomena of  gravitation,  of  optics^  of  electricity  and 
magnetism,  physicists  have  thus  been  led  to  con- 
sider a  series  of  media,  the  discrepancies  of  which 
Hannequin1  found  pleasure  in  exposing,  but  all  of 
which  have  in  the  end  become  fused  together  in 
Maxwell's  dielectric  ether. 

It  was  the  consideration  of  the  ether  that  per- 

1  Hannequin,  Essai  critique  sur  1'hypothese  des  atomes  dans  la 
science  contemporaine,  p.  178-224. 


64  PHILOSOPHY    AND    THE    NEW    PHYSICS 

mitted  a  marked  reduction  of  the  number  of  pri- 
mary principles  required  for  an  explanation  of 
things.  At  the  beginning  of  the  nineteenth  cen- 
tury the  existence  of  eight  energetic  imponderable 
agents  outside  of  matter  was  commonly  assumed: 
the  electric  fluids,  positive,  negative,  and  neutral ; 
the  magnetic  fluids,  south,  north,  and  neutral;  the 
caloric,  and  the  luminous  fluid.  Gradually  these 
agents  have  disappeared:  heat  has  turned  out  to 
be  the  sensible  manifestation  of  the  internal  agita- 
tion of  the  molecules  of  bodies.  Inspired  by  Fres- 
nel's  ideas  Maxwell  tried  to  explain  the  electric, 
magnetic  and  optical  phenomena  that  ceased  to  be 
attributed  to  particular  fluids  by  starting  from  the 
mechanical  properties  of  the  ether.  Electrostatic 
phenomena,  for  example,  seemed  to  him  to  be 
explained  by  the  deformations  of  the  ether.  Static 
charges  of  electrified  bodies  have  merely  a  fictitious 
existence :  they  are  the  locus  of  the  ends  of  the  lines 
or  tubes  of  force  corresponding  to  the  deformations 
of  the  ether.  These  deformations  subject  the 
conductors  to  pressures  and  tensions  forcing  them 
to  approach  each  other  or  to  move  apart,  the  electro- 
static energy  being  nothing  but  the  potential 
energy  of  deformation  of  the  ether.  The  electro- 
kinetic  phenomena  are  explained  by  disturbances 
of  the  ether.  The  electric  current  is  not  a  phenome- 
non taking  place  in  the  conductor  but  a  state 
of  motion  of  the  adjoining  ether,  the  character, 
direction,  and  intensity  of  which  are  determined 
by  the  geometrical  and  physical  properties  of  the 


DEMATERIALIZATION    OF   MATTER  65 

conductor,  the  energy  of  the  electric  current  cor- 
responding to  the  kinetic  energy  of  the  surrounding 
ether.  There  exist  only  -two  realities,  matter  and 
ether,  the  former  of  which  acts  like  a  supernumer- 
ary; the  ether,  in  which,  in  the  form  of  static  defor- 
mations, the  electric  energy  is  stored,  and  in  which, 
in  the  form  of  disturbances,  the  radiant  energy  is 
propagated,  appears  more  and  more  as  the  only 
active  medium  taking  part  in  the  production  of  the 
phenomena. 

Wherein  has  the  electronic  theory  strengthened 
or  weakened  this  idea,  which  satisfies  our  taste  for 
simplicity?  It  seems  at  first  that,  in  addition  to 
matter  and  ether,  it  restores  one  of  the  old  agents, 
the  negative  electricity,  no  longer  conceived,  however, 
as  a  continuous  fluid  but  as  a  substance  endowed 
with  corpuscular  structure,  not  as  an  imponderable 
but  as  endowed  with  inertia.  In  fact,  we  have 
the  phenomena  of  electrolysis,  which  show  us  a 
monovalent  ion  carrying  a  well  defined  quantity 
of  electricity  e,  which  is  always  the  same;  a  bivalent 
ion  carrying  a  quantity  of  electricity  2e  and  so  on. 
Now  this  elementary  charge,  which  appears  to  be 
indivisible  like  an  atom,  is  precisely  that  which  is 
found  again,  but  without  material  support,  in  the 
negative  electrons,  issuing  from  the  cathode  dis- 
integration in  Crookes'  tubes,  or  from  the  atomic 
disintegration  in  the  0  rays  of  radium,  or  the  kinetic 
agitation  in  the  negative  emissions  of  heated  or 
illuminated  conductors  (Edison's  and  Hertz's  phe- 
nomena). These  charges  can  no  longer  play  the 


66  PHILOSOPHY   AND    THE    NEW    PHYSICS 

part  of  pure  fictions,  by  being  placed  geometrically 
at  the  ends  of  lines  or  tubes  of  force  constituted  of 
deformations  of  the  ether:  they  have  a  physical 
existence,  a  structure  and  inertia  of  their  own.  In 
these  grains  of  electricity,  and  not  in  the  mechanical 
states  of  the  ether,  the  initial  cause  of  electric  and 
magnetic  phenomena  must  be  sought.  The  elec- 
tric current,  for  example,  has  not  its  seat  in  the 
ether  but  in  the  conductor;  it  consists  of  a  mass 
motion  of  the  free  electrons  of  the  metal,  superim- 
posed on  their  chaotic  kinetic  agitation,  like  the 
flow  of  a  gas  in  a  pipe:  there  is  no  longer  a  con- 
duction current  due  to  the  ether,  but  merely  a 
convection  current  due  to  electrified  particles  in 
motion. 

But  at  the  very  time  when  the  discoveries  of 
contemporary  physics  seem  of  necessity  to  increase 
the  number  of  primary  principles,  by  a  return  to  the 
old  agents,  through  assuming  grains  of  resinous 
(negative)  electricity,  their  offspring,  the  electronic 
theory,  works  an  inverse  reduction  by  destroying 
the  concept  of  matter,  which  from  this  point  of  view 
has  merely  a  gross  semblance  of  reality.  According 
to  this  theory,  the  molecular  and  atomic  structures 
constituting  bodies  are  reduced  to  electronic  archi- 
tecture, the  electrons  being  positive  and  negative, 
or  simply  negative,  and  their  inertia  being  entirely 
of  electromagnetic  origin  and  due  to  the  self-in- 
duction of  the  convection  currents  that  they  produce 
by  their  displacement.  Matter,  ceasing  to  corre- 
spond to  a  distinct  reality,  is  resolved  into  grains  of 


DEMATERIALIZATION    OF   MATTER  67 

electricity   and   these,    according   to    the   English 
school,  become  subtilized  into  mere  ether  cavities. 

Rearming  themselves  with  the  ideas  of  Faraday 
and  Maxwell,  the  English  physicists,  and  the  most 
famous  of  them,  J.  J.  Thomson,  regard  the  inertia 
of  the  electron  as  due  to  the  ether  surrounding  it. 
An  electron  at  rest  is  a  surface  charge  without  mate- 
rial support,  and  may  be  considered  as  a  cavity  in 
the  ether.  This  cavity  is  the  center  from  which  the 
electric  lines  of  force  constituting  the  electro- 
static field  of  the  electron  diverge.  The  ether  ad- 
heres to  these  lines  of  force,  so  that  the  electron  can 
not  move  without  displacing  it.  The  inertia  of  the 
electron  results  from  the  inertia  of  the  entrained 
ether,  which  alone  opposes  its  motion.  Knowing 
the  volume  and  the  masfe  of  an  electron,  the  density 
of  the  ether  adhering  to  it  may  be  calculated;  it  is 
found  to  be  equal  to  about  2000  million  times  the 
density  of  lead.  Matter  ceases  to  exist,  since,  being 
composed  of  electrons,  the  sole  reason  we  have  to 
believe  in  it,  namely  its  inertia,  does  not  properly 
belong  to  it,  but  is  borrowed  from  the  ether.  Elec- 
tricity likewise  disappears  as  a  substance  with  an 
existence  of  its  own,  since  the  electrons  are  reduced 
to  cavities  in  the  ether.  Two  principles  only  sur- 
vive, ether  and  empty  space,  of  one  of  which  the 
ancients  would  have  said  that  it  is  the  non-being 
and  consequently  that  it  does  not  exist.  The 
world  is  merely  a  bubble  of  ether  in  the  non-thing. 

This   theory   of   the    disincarnation    of   matter, 
leading  to  a  complete  etherization,  should,  in  spite 


68  PHILOSOPHY   AND   THE    NEW   PHYSICS 

of  its  alluring  aspect,  be  taken  with  considerable 
caution.  It  is  threatened  with  downfall  on  account 
of  the  concept  that  forms  its  base,  that  of  an  ether 
endowed  with  mechanical  properties,  the  hypo- 
thetical existence  of  which  seems,  moreover,  to  be 
contradictory. 

To  fulfill  its  office  the  ether  must  accumulate 
the  mutually  exclusive  properties  of  solids  and 
fluids.  It  must  behave  like  an  elastic  solid,  en- 
dowed with  a  rigidity  surpassing  that  of  steel  in 
order  to  transmit  nearly  instantaneously  the  trans- 
verse vibrations  of  light;  it  must  behave  like  a 
fluid  with  a  density  much  less  than  that  of  the 
lightest  gas,  in  order  not  to  retard  the  translatory 
motion  of  the  stars  and  not  to  rob  them  of  their 
atmosphere;  but  in  the  neighborhood  of  the  elec- 
trons it  must  have  a  density  far  surpassing  that 
of  lead.  All  this  is  incomprehensible  and  no  one 
can,  under  the  plea  of  thinking  in  terms  of  the 
ether,  evade  thinking  according  to  the  law  of 
contradiction. 

If  the  ether  exists,  it  is  incapable  of  motion, 
as  is  proved  by  the  impossibility  .  of  reconciling 
Fizeau's  experiment  with  Hertz's  hypothesis  of  a 
complete  entrainment  of  the  ether  by  matter  in  mo- 
tion, and  the  impossibility  of  reconciling  the  prin- 
ciple of  action  and  reaction  with  FresneFs  and 
Fizeau's  hypothesis  of  a  partial  entrainment  of  the 
ether.  But,  if  the  ether  is  incapable  of  motion,  our 
laboratories  and  our  instruments  are  continuously 
traversed  by  an  ether  current,  the  velocity  of  which 


DEMATERIALIZATION    OF    MATTER  69 

is  equal  to  and  opposite  to  that  of  the  earth  and 
varies  as  a  function  of  it.  Such  a  current  would 
exert  a  considerable  influence  on  electromagnetic 
and  optical  phenomena.  Now  the  experiments 
undertaken  to  show  the  absolute  motion  of  the  earth 
with  respect  to  the  ether,  with  which  a  privileged  set 
of  reference  axes  might  be  connected,  show  that 
there  is  none.  The  hypothesis  of  an  immovable 
ether  is  in  its  turn  contradicted  by  the  relativity 
principle. 

But  there  is  more  than  that.  Neither  Max- 
well nor  any  one  after  him  has  succeeded  in  giving 
a  clear  and  distinct  mechanical  representation  of 
the  deformations  and  disturbances  of  the  ether  that 
would  produce  the  electric  and  magnetic  phe- 
nomena. In  attempting  it  he  arrived  at  a  concep- 
tion so  strange,  that  of  a  cellular  ether  formed  of  two 
substances  one  of  which  was  impregnated  with  the 
other  like  a  sponge  soaked  with  water,  that  he  did 
not  make  it  play  a  part  in  his  large  Treatise  on 
Electricity  and  Magnetism.  Recently  Witte1  has 
shown,  by  a  very  complete  analysis,  that  the  proper- 
ties of  the  electromagnetic  field  cannot  be  explained 
by  the  aid  of  classical  mechanics  with  any  supple- 
mentary hypothesis,  if  we  assume  the  hypothesis  of 
a  continuous  ether,  and  he  rejects  as  improbable 
that  of  a  discontinuous  ether.  To-day  we  see  the 
underlying  reason  of  this  impossibility  in  the  rela- 

1  Cf.  Witte,  Ueber  den  gegenwartigen  Stand  der  Frage  nach 
einer  mechanischen  Erklamng  der  elektrischen  Erscheinungen, 
Berlin,  1906. 


70  PHILOSOPHY    AND    THE    NEW    PHYSICS 

tivity  principle.  The  Lorentz  group,  for  transfor- 
mations of  which  the  form  of  the  equations  of 
electromagnetism  remains  unaltered,  excludes  the 
Galileo  group,  for  the  transformations  of  which  the 
form  of  the  equations  of  classical  dynamics  is 
conserved.  Mechanical  explanations  of  electric 
phenomena  are,  therefore,  definitely  condemned. 

Lastly,  we  shall  see  that  there  are  reasons  for 
believing  that  radiation  is  not  propagated  by 
means  of  a  hypothetical  medium,  but  projected  into 
empty  space  in  the  form  of  discontinuous  elemen- 
tary quantities,  energy  atoms,  called  quanta.  With 
this  return  to  an  emission  theory  the  most  con- 
vincing argument  in  favor  of  the  ether,  the 
consideration  of  which  becomes  superfluous, 
disappears.  This  is  expressed  by  Einstein:1  "The 
electric  and  magnetic  fields  that  constitute  light  no 
longer  appear  as  states  of  a  hypothetical  medium, 
but  as  individual  realities,  which  the  luminous 
sources  send  into  space  as  in  Newton's  emission 
theory." 

If  we  renounce  the  mechanical  ether  of  Faraday, 
of  Maxwell,  of  Lord  Kelvin  and  of  Sir  O.  Lodge, 
and  consider  nothing  but  an  absolutely  empty 
space,  at  every  point  of  which  an  electric  and  a 
magnetic  field  may  be  superimposed,  then  the 
idea  of  the  dematerialization  of  matter  gives  place 
to  that  of  a  materialization  of  energy.  The  only 
reality  that  is  positively  observable  and  empirically 

1  Einstein,  Phys.  Zeitschr,  vol.  x,  1909,  p.  849.  Cf.  Campbell, 
Phil.  Mag.  1910,  p.  981. 


DEMATERIALIZATION    OF    MATTER  71 

demonstrable  is  the  energy  that,  at  any  time,  is 
localized  in  a  region  of  space  and  corresponds  to 
the  two  fields,  electric  and  magnetic,  which  are 
at  the  moment  superimposed  there,  its  density 
per  unit  volume  being  proportional  to  the 
squares  of  these  fields.  Nothing  prevents  us  from 
considering  energy  as  a  substance,  endowed  in 
itself  with  existence,  without  the  aid  of  any  sub- 
stratum whatever.  It  is  therefore  convenient, 
instead  of  reducing  the  inertia  of  the  electron  to 
the  agitation  of  the  ether,  to  attribute  it  to  the 
energy  accumulated  around  it,  which  forms  its 
electromagnetic  wave  system.  Moreover  we  need 
not  picture  the  electron  as  a  spherical  cell  of  two 
millionths  of  a  w  with  a  surface  charge.  It  is 
more  natural  to  suppose  either  that  the  density 
of  this  charge  gradually  diminishes  from  the  center 
of  the  sphere  outwards,  so  that  the  electron  does 
not  possess  a  definite  surface,  or  that  there  is 
a  uniform  distribution  of  the  electric  density  in 
the  inside  of  the  volume  of  the  sphere,  which  implies 
a  definite  contour:  in  the  latter  case  the  same  for- 
mulae are  obtained  as  in  the  case  of  a  surface 
distribution,  with  the  single  difference  that  all 
quantities  that  play  a  part  in  the  equations  are 
multiplied  by  the  factor  %. 

To  sum  up,  a  moving  electron  appears  to  us 
as  a  circumscribed  region  of  space,  where  there  is 
to  be  found  accumulated  electromagnetic  energy  in 
the  form  of  fields,-  the  intensity  and  distribution 
of  which  vary  as  a  function  of  the  velocity.  The 


72  PHILOSOPHY    AND    THE    NEW    PHYSICS 

mass  of  an  electron  can  not  be  attributed  to  a 
material  support  that  does  not  exist,  nor  to  the  sur- 
rounding ether,  the  existence  of  which  is  hypothet- 
ical, but  it  is  due  to  its  own  energy,  which  consti- 
tutes its  only  substantial  reality.  But  if  energy  is 
inert  it  is  endowed  with  mass,  consequently  with 
weight  in  proportion  thereto,  and,  possessing  struc- 
ture, it  becomes  a  materialized  body,  while  matter 
is  refined  away. 

If  now,  in  conformity  with  Lorentz's  theory, 
the  molecular  structures  that  constitute  bodies  are 
reducible  to  assemblages  of  electrons,  and  if  the 
electron  is  inert  only  because  of  the  energy  which 
it  possesses,  material  systems  are  themselves  en- 
dowed with  mass  only  in  proportion  to  the  energy 
that  they  contain.  Mass  becomes  a  quantity  that 
measures  their  internal  energy,  and,  as  foreseen  by 
Ostwald,  the  concept  of  matter  is  subsumed  under 
the  more  general  one  of  energy. 


CHAPTER  V 
THE  INERTIA  OF  ENERGY 

12.    THE  MATERIALIZATION  OF  ENERGY. 

The  conclusion  stated  at  the  end  of  the  last  chapter 
appeared  as  almost  an  immediate  consequence  of 
a  paper  by  Henri  Poincare1  on  the  longitudinal 
contraction  of  an  electron  in  motion.  Taking  the 
older  point  of  view,  that  of  the  partisans  of  the 
mechanical  ether,  though  the  point  of  view  thus 
taken  matters  little  in  this  connection,  he  showed 
that  this  contraction  is  exactly  that  demanded  for 
the  maintenance  of  its  equilibrium  on  the  assumption 
that  the  surface  charge  carried  by  the  moving 
electron,  the  elements  of  which  tend  to  separate 
because  of  their  natural  repulsion,  is  maintained 
by  a  constant  pressure  of  the  ether.  Assuming 
this  uniform  pressure,  the  equilibrium  configuration 
of  an  electron  at  rest  is  that  which  makes  the 
potential  energy  of  the  actions  superimposed  on 
it  —  electrostatic  repulsions  and  Poincare  pressure  — 
a  minimum.  If  its  shape  is  that  of  a  sphere  of 
radius  a  the  total  potential  energy  of  an  electron 
at  rest  in  equilibrium  is  given  by 

(7)  E   •         *  *  * 

h° 


1  H.  Poincare,  La  theorie  de  Lorentz  et  le  principe  de  reaction 
(Archives  neerlandaises,  1900,  p.  252-278). 

73 


74  PHILOSOPHY   AND,  THE    NEW    PHYSICS 

•  A  comparison  of  this  expression  with  that 
of  the  initial  electromagnetic  mass  m0  (5)  leads 
at  once  to  the  relation 

(8)  Wo    =    KQHQ  EQ. 

According  to  the  relation  between  the  two 
coefficients  KQ  and  ^o  deduced  by  Maxwell  from  the 
comparison  of  the  two  systems  of  C.  G.  S.  units, 
the  electrostatic  and  electromagnetic,  namely, 


where  V  represents  the  velocity  of  light,  the  ex- 
pression (8)  becomes 

Tjl 

(9)  Wo  =  Y* 

The  initial  electromagnetic  mass  of  an  electron 
at  rest  is  equal  to  its  total  potential  energy  divided 
by  the  square  of  the  velocity  of  light.  As  the  potential 
energy  represents  the  only  energy  that  an  electron 
at  rest  can  have,  it  is  seen  immediately  that,  the 
velocity  of  light  being  taken  as  unity,  the  mass  of  an 
electron  at  rest  is  equal  to  its  total  energy,  of  which 
it  may  serve  as  a  measure. 

This  result  may  be  generalized.  If  the  elec- 
tronic theory  of  matter  were  confirmed,  it  would  be 
applicable  to  all  material  systems  at  rest,  since 
they  could  be  reduced  to  assemblages  of  electrons 
without  material  support.  However  it  may  be  con- 
cerning this  last  point  and  postponing  the  question 
of  the  structure  of  the  positive  centers,  whether 
material  or  not,  Lorentz  has  shown  that  the  rela- 


MATERIALIZATION    OF    ENERGY  75 

tivity  principle  requires:  (1)  the  longitudinal  con- 
traction  of   all   bodies   in   the   direction   of   their 


translation  in  the  ratio  Vl  —  02;  (2)  that  the  change 

m0 
of  mass  with  the  velocity,  m  =     ,r-^=^,  established 

first  of  all  for  electromagnetic  inertia,  applies  in 
general  to  all  bodies,  as  if  their  mass,  like  the  forces 
of  •  elasticity  and  cohesion,  were  purely  of  electro- 
magnetic origin.  It  follows  therefrom  that  the 
relation  (9)  must  be  applied  to  all  material  systems 
at  rest  as  if  the  electronic  theory  were  correct. 
This  relation  may  be  extended  to  all  bodies 
and  material  systems  in  motion.  The  same  rela- 
tion that  exists  between  the  masses  m0  and  m  of 
the  same  body  observed  by  observers  00  at  rest 
with  respect  to  it  and  by  observers  0i  in  motion, 
must  exist,  by  virtue  of  the  relativity  principle, 
between  the  energies  E0  and  E  of  the  same  system 
observed  simultaneously  by  00  and  Oi,  so  that  we 
have 


By  virtue  of  (6)and  (10),  the  relation  (9)  leads 


A 


to  the  generalization  already  stated,  namely, 
(11)  M  =  ~ 


The  quantity  Vl  —  j32  being  always  less  than  one, 
it  follows  from  (10)  that  the  energy  of  a  body  set 
into  motion  without  deformation  is,  for  observers 
connected  with  it,  greater  than  when  it  is  at  rest. 


76  PHILOSOPHY   AND    THE    NEW    PHYSICS  ' 

The  difference  represents,  by  definition,  the  kinetic 

EQ 

energy;  and  the  two  terms  "^        and   mQV2,   of 


which  it  is  the  difference,  are  nothing  but  two  meas- 
ures of  -the  total  energy  of  the  same  body,  made  suc- 
cessively by  observers  in  motion  and  at  rest. 

To  sum  up,  the  existence  of  convection  cur- 
rents, foreseen  theoretically  by  Maxwell  and  realized 
experimentally  by  Rowland,  led  J.  J.  Thomson, 
Max  Abraham,  and  Lorentz  to  study  theoretically 
the  laws  of  variation  of  the  inertia  of  an  elec- 
trified particle  in  motion.  The  discovery  of  cath- 
ode particles  permitted  Kaufmann  and  Bucherer 
to  verify  these  theoretical  anticipations  and  to 
reveal  the  existence  of  grains  of  resinous  (negative) 
electricity  or  electrons,  the  inertia  of  which  is  solely 
of  electromagnetic  origin  and  obeys  the  preceding 
theoretical  laws.  Starting  from  this  result  Pom- 
care  has  shown  that  the  initial  mass  of  an  electron 
in  equilibrium  and  at  rest  is  equal  to  its  total 
potential  energy  divided  by  the  square  of  the  veloc- 
ity of  light.  The  principle  of  relativity  requires, 
then,  that  this  result  be  extended  to  all  systems  of 
bodies  at  rest  and  in  motion,  so  that  the  formula 
M  =  E/V2,  thereafter  fundamental,  shall  hold  for 
them.  Taking  the  velocity  of  light  as  unity,  this 
formula  states  that  the  mass  o/  a  body  is  equal  to  its 
total  energy,  of  which  it  may  serve  as  a  measure,  and 
consequently  energy  is  inert. 

The  decisive  arguments  in  favor  of  the  inertia  of 
energy  are,  however,  drawn  from  considerations 


MATERIALIZATION    OF   ENERGY  77 

of  another  kind.  They  result  from  the  necessity  of 
reconciling  Maxwell's  pressure  of  radiation  with  the 
principle  of  relativity  and  with  that  of  action  and 
reaction  or  of  the  conservation  of  momentum  in  a 
closed  system.1 

Maxwell,  by  starting  from  the  electromagnetic 
theory  of  light,  and  Bartoli,  by  starting  from  the 
principles  of  thermodynamics,  foresaw  theoretically, 
and  Lebedew  verified  experimentally,  that  all  radi- 
ation exerts  a  backward  pressure  on  the  source  that 
emits  it  in  a  single  direction  and  a  forward  pressure 
on  an  obstacle  that  absorbs  it :  this  is  what  is  called 
the  pressure  of  radiation.  The  inertia  of  energy  is  a 
consequence  of  the  existence  of  this  pressure,  and 
brings  up  the  metaphysical  problem  of  the  action  of 
an  imponderable  on  a  ponderable  in  a  particularly 
acute  form. 

Let  us  consider  first  a  material  system  the  motions 
of  which  are  due  solely  to  internal  actions,  such  as  a 
firearm  and  its  projectile.  When  the  shot  takes 
place  the  gun  undergoes  a  recoil,  that  is  to  say,  takes 
up  a  certain  momentum  which,  counted  negatively, 
represents  a  loss;  the  projectile  is  shot  forward  and 
acquires  a  momentum  which,  counted  positively,  is 
equal  to  that  lost  by  the  gun.  The  conservation  of 
the  total  momentum  of  the  system  holds  at  every 
instant,  and  consequently  there  is  no  motion  of  the 
center  of  gravity  of  the  system.  The  conservation 

1  Cf.  A.  Einstein,  Ann.  der  Phys.  vol.  xviii,  1905,  p.  639.  P. 
Langevin,  L'inertie  de  Tenergie  et  ses  consequences  (Journal  de 
Physique,  juillet  1913,  p.  553  et  seq). 


78  PHILOSOPHY   AND   THE    NEW   PHYSICS 

of  momentum  is  but  a  natural  consequence  of  the 
instantaneous  equality  of  action  and  reaction.  The 
gun  recoils  because,  while  it  acts  on  the  projectile, 
the  latter  reacts  in  turn  equally  on  it. 

Let  us  now  consider  a  material  source  that  radi- 
ates unsymmetrically  in  a  single  direction,  such  as  a 
lamp  provided  with  a  reflector  or  a  Hertzian  exciter 
at  the  center  of  a  parabolic  mirror.  At  the  instant 
of  the  emission  the  source  recoils  as  a  consequence 
of  the  pressure  of  radiation :  there  is  a  loss  of  momen- 
tum. If  the  radiation  encounters  an  obstacle  that 
absorbs  it,  it  will  communicate  to  it  an  impulse, 
that  is,  a  momentum  equal  to  that  lost  at  departure 
by  the  source.  The  action  experienced  by  the 
obstacle  will  be  equal  in  magnitude  to  the  reaction 
undergone  by  the  source. 

Does  this  mean  that  the  principle  of  the  conserva- 
tion, of  momentum  or  of  action  and  reaction  is  safe- 
guarded? Certainly  not,  for  it  is  not  so  at  every 
instant  from  the  start.  A  certain  interval  of  pro- 
pagation elapses  between  the  time  when  the  radia- 
tion is  emitted  and  that  when  it  is  absorbed,  during 
which  the  momentum  lost  by  the  source  and  the 
reaction  that  the  latter  undergoes  remain  uncompen- 
sated.  This  compensation  would  never  take  place 
if  the  radiation  were  propagated  to  infinity  without 
encountering  matter  absorbing  it.  In  this  case 
there  would  be  a  definite  loss  of  momentum  and  the 
center  of  gravity  of  the  system  formed  by  the  source 
and  the  radiation  would  take  an  absolute  motion, 
which  is  contrary  to  the  relativity  principle. 


MATERIALIZATION    OF    ENERGY  79 

If  this  principle  is  to  be  safeguarded  and  at  the 
same  time  those  of  the  conservation  of  momentum 
and  of  action  and  reaction,  the  system  source- 
radiation  must  be  assimilated  to  the  material 
system  of  the  fire-arm  and  its  proj  ectile.  The  radia- 
tion must  be  treated  as  a  material  projectile,  that  is, 
it  must  be  regarded  as  representing  a  certain  mo- 
mentum equal  to  that  lost  by  the  source,  so  that  the 
reaction  that  the  source  undergoes  is  the  natural 
effect  of  the  action  exerted  on  it;  only  in  this  case  will 
the  center  of  gravity  of  the  system  remain  fixed  and 
the  relativity  principle  be  satisfied.  This  is  what 
Henri  Poincare  has  not  hesitated  to  do.  He  was 
the  first  one  to  introduce  the  idea  of  electro-magne- 
tic momentum  of  radiation  to  save  Newton's 
principle  of  action  and  reaction,  which  is  sacrificed 
in  Lorentz  's  theory. 

But  momentum  means,  by  definition,  mass  in 
motion,  in  virtue  of  the  vectorial  relation 

g  =  mv. 

The  projectile  carries  away  in  its  motion  a  part 
of  the  initial  mass  of  the  loaded  fire-arm,  which  is 
diminished  by  just  so  much:  that  is  why  we  have 
instantaneous  equality  of  action  and  reaction, 
conservation  of  momentum  and  a  stationary  center 
of  gravity  of  the  system.  Hence,  if  radiation  is  a 
vehicle  of  momentum,  it  must  carry  away  with  it  a 
part  of  the  initial  mass  of  the  radiating  material 
source.  It  must  be  possible  to  assimilate  literally 
the  sdurce-radiation  system  to  that  of  the  firearm- 


80  PHILOSOPHY   AND   THE    NEW   PHYSICS 

projectile,  as  also  in  the  case  of  a  radium  atom  dur- 
ing its  transmutation  when  it  spontaneously  divides 
into  a  helium  atom  and  a  niton  atom  by  a  sudden 
explosion  that  projects  the  helium  atom  and  the 
niton  atom  with  equal  momentum  in  opposite 
directions.  After  we  have  discussed  the  structure 
of  radiant  energy,  which  tends  to  make  the  radiation 
assume  the  characteristics  of  a  corpuscular  emission, 
the  preceding  assimilation  will  appear  less  bold. 
Hence  if  radiation  carries  away  momentum  it  must, 
just  like  electric  energy,  possess  electromagnetic 
mass  apart  from  any  material  substratum. 

Let  us  determine  quantitatively  the  momentum 
and  the  Maupertuisian  mass  that  must  be  thus 
attributed  to  radiant  energy,  to  safeguard  the 
principle  of  action  and  reaction  and  the  relativity 
principle. 

In  the  case  of  a  plane  wave,  the  electromagnetic 
momentum  is  in  the  direction  of  propagation  and 
at  right  angles  to  the  plane  of  the  wave  containing 
the  two  fields,  the  electric  and  the  magnetic.  By 
taking  into  account  the  fact  that  in  this  case  the 
two  fields  are  mutually  perpendicular,  it  may  be 
shown  that  the  density  g,  per  unit  volume,  of  the 
momentum  has  the  value 


where  V  represents  the  velocity  of  propagation  of 
the  plane  wave,  which  is  equal  to  that  of  light. 
Since  on  the  other  hand,  the  density,  per  unit 


MATERIALIZATION    OF    ENERGY  81 

volume,  of  the  electromagnetic  energy  has,  by  virtue 
of  (7),  the  value 

#      -^  +*£-'-  3* 

the  result  for  the  density  of  momentum  becomes 

(14)  g  =  ~  • 

The  electromagnetic  momentum  per  unit  volume  is 
equal  to  the  electromagnetic  energy  divided  by  the 
velocity  of  light. 

To  this  momentum  there  corresponds  a  Mau- 
pertuisian  mass  by  virtue  of  the  vectorial  relation 
g  =  mv. 

The  magnitude  of  this  mass  is,  by  definition,  the 
momentum  divided  by  the  velocity,  which,  in  this 
case,  is  that  of  light, 


If  we  replace  g  by  its  value  E/V  from  the  relation 
(14),  we  get 

(15)  M=y-* 

Free  radiation  has  a  mass  equal  to  its  energy 
divided  by  the  square  of  the  velocity  of  light.  Since  all 
forms  of  energy  may  be  transformed  into  radiant 
energy,  the  preceding  result  may  be  generalized  as 
follows:  every  form  of  energy  E  possesses  a  certain 
coefficient  of  inertia  determined  by  the  preceding 
formula.  Contrary  to  the  fundamental  principle 


82  PHILOSOPHY   AND    THE    NEW    PHYSICS 

of  the  dualistic  theory  energy  of  any  form  whatever 
is  inert. 

The  identity  of  the  formulae  (11)  and  (15)  shows 
that  the  mass  of  a  body  and  radiant  energy  are 
equivalent  quantities,  capable  of  being  converted 
one  into  the  other,  as  heat  and  mechanical  work  are. 
If  a  body  radiates  energy,  the  radiation  emitted 
carries  away  a  part  AE/V2  of  its  initial  mass,  and 
when  an  obstacle  absorbs  this  radiation  its  previous 
mass  is  increased  by  the  entire  Maupertuisian  mass 
AE/V2  of  the  absorbed  radiation,  whence: 

Any.  change  AE  of  the  internal  energy  of  a  material 
system,  due  to  emission  or  absorption  of  radia- 
tion, is  accompanied  by  a  proportional  variation 
of  its  mass  in  accordance  with  the  relation: 

(16)  AM  = 


V 


If  we  examine  closely  this  enunciation  of  the 
proposition  as  to  the  variation  of  the  mass  of  bodies 
as  function  of  their  velocity,  it  follows,  contrary 
to  the  third  and  fourth  postulates  of  the  dualistic 
doctrine,  that:  the  mass  of  a  body  is  not  invariable; 
it  increases  or  it  decreases  according  as  the  body  ab- 
sorbs or  radiates  energy,  and  as  it  is  in  motion  or  at 
rest  with  respect  to  the  system  to  which  it  is  referred. 

The  last  postulate  of  the  dualistic  theory  is 
therefore  necessarily  unsound.  In  an  isolated  sys- 
tem, the  different  parts  of  which  exchange  energy, 
the  individual  masses  of  the  bodies  present  are  not 
conserved;  it  is  only  the  total  inertia  of  the  system 


MATERIALIZATION    OF    ENERGY  83 

(the  constant  sum  of  the  variable  inertia  of  the 
bodies  and  the  variable  inertia  of  the  radiation) 
that  is  conserved,  provided  the  system  does  not  per- 
mit any  exchange  with  the  outside.  The  principle 
of  the  conservation  of  mass  of  material  bodies  is 
no  longer  valid  by  itself:  it  is  replaced  by  the  more 
general  principle,  which  alone  is  valid,  of  the  con- 
servation of  the  total  inertia  of  an  isolated  system. 

How  are  we  to  evaluate  this  total  inertia?  An 
inspection  of  (9)  and  (10)  shows  that  the  total 
energy  of  a  body,  at  rest  as  well  as  in  motion,  is 
equal  to  the  product  of  its  mass  by  V2.  If  the 
velocity  of  light  in  a  vacuum  is  taken  as  the  funda- 
mental unit,  it  follows  that  the  mass  of  a  body  is  equal 
to  its  total  energy,  a  statement  that  translates  the 
identity  of  the  nature  of  mass  and  energy  into  a  nu- 
merical equality;  or,  better  still,  the  mass  of  a  body 
measures  its  internal  energy. 

The  total  inertia  of  an  isolated  system,  which 
neither  loses  nor  receives  energy,  is,  therefore,  equal 
to  its  total  energy:  the  internal  energy  of  the  bodies 
present,  the  kinetic  energy  of  these  bodies,  the  energy 
of  free  radiation.  The  principle  of  the  conservation 
of  the  total  inertia  of  a  system  goes  back,  therefore, 
to  the  principle  of  the  conservation  of  energy,  into 
which  the  principle  of  the  conservation  of  mass  is 
henceforth  absorbed.  In  the  new  dynamics  of 
relativity,  there  exist  only  two  fundamental  laws 
of  invariance :  that  of  the  conservation  of  energy  and 
that  of  the  conservation  of  momentum.  The  first 
leads  to  the  assumption  of  energy  localized  outside 


84  PHILOSOPHY   AND    THE    NEW   PHYSICS 

of  bodies;  the  second  leads  to  the  assumption 
of  the  existence  of  electromagnetic  momentum  in 
free  radiation  and  consequently  of  the  inertia  of 
energy.  These  two  laws  are  not  independent.  If 
we  were  to  adopt  Minkowki's  terminology  of  the 
"  world' '  where  the  phenomena  are  referred  to  four 
interchangeable  axes,  implying  four  homogeneous 
coordinates,  three  of  space  and  one  of  time,  these 
two  laws  would  appear  as  two  different  aspects  of 
one  single  law,  that  of  the  conservation  of  the  world 
impulse. 

Lastly,  as  a  consequence  of  the  exact  proportion- 
ality between  mass  and  weight  shown  by  Eotvos, 
from  the  inertia  of  energy  follows  its  weight  in 
proportion  thereto:  a  change  of  internal  energy 
would  at  the  same  time  be  accompanied  by  a  change 
of  mass  and  a  change  of  weight.  Since  it  is  easier 
to  measure  the  weight  than  the  mass  of  a  body,  the 
weight  of  a  body  might  serve  to  measure  its  internal 
energy. 

13.    THE     EVALUATION     OF    THE    INTERNAL    ENERGY 
OF  BODIES  AND  THE  VARIATIONS  OF  MASS. 

From  the  inertia  of  energy  the  abandonment  of 
the  dualistic  theory  and  numerous  special  conse- 
quences result. 

1.  Evaluation  of  the  internal  energy  of  bodies. 

Whenever  a  body  loses  heat  or  changes  its  dimen- 
sions under  the  influence  of  internal  actions  alone, 
it  performs  thermal  or  mechanical  work  that 
corresponds  to  a  loss  of  some  of  its  energy.  The 


INTERNAL    ENERGY  85 

internal  energy  of  a  body  was  formerly  defined  as 
the  total  work  it  could  perform  as  a  consequence 
of  cooling  without  limits,  or  of  extension  or  con- 
traction without  limits,  according  as  the  molecular 
forces  are  attractive  or  repulsive.  There  was  no 
way  of  evaluating  such  a  quantity  of  energy; 
changes  only  of  internal  energy  could  be  measured 
by  the  work  performed  in  starting  from  an  initial 
condition. 

On  the  other  hand  the  formula  ra0  =  E/V2  pro- 
vides a  very  simple  method  of  evaluating  this  energy 
of  intermolecular  and  intra-atomic  nature.  It  is 
equal  to 


for  a  body  at  rest  for  those  who  observe  it.  This 
relation  shows  that  a  gram  of  matter  at  rest  and 
at  the  temperature  of  the  absolute  zero  corresponds 
to  the  presence  of  an  internal  energy  equal  to  9  X 
1020  ergs,  that  is,  an  energy  equivalent  to  the  heat 
furnished  by  the  combustion  of  3  X  109  grams  or 
3,000,000  kilograms  of  anthracite. 

Let  us  call  the  energy  of  a  body  thus  evaluated 
for  the  temperature  T  =  0  and  the  state  of  rest 
latent  energy.  This  enormous  energy  is  nearly 
entirely  of  intra-atomic  nature.  In  fact,  at  the 
absolute  zero  the  degrees  of  freedom  of  the  mole- 
cules are,  as  it  were,  anchylosed  by  the  frost.  On 
the  other  hand  the  physical  molecular  forces  and 
the  chemical  atomic  forces  put  in  action  a  quantity 
of  energy  only  very  small  compared  with  this 


86  PHILOSOPHY   AND    THE    NEW    PHYSICS 

enormous  reserve  of  latent  energy,  as  can  easily  be 
calculated.  The  changes  of  mass  'that  result  from 
the  presence  or  absence  of  heat  or  kinetic  energy  or 
the  presence  of  radiation  within  a  body  are  practi- 
cally imperceptible,  except  in  the  case  of  radioactive 
transformations,  where  the  intra-atomic  energy 
again  comes  into  play. 

2.  Change  of  mass  with  temperature. — The  same 
portion  of  matter,  taken  at  twro  different  tempera- 
tures, may  pass  from  one  to  the  other  by  emission 
or  absorption  of  radiant  heat.  The  change  of 
mass  resulting  therefrom  may  be  evaluated  by 
dividing  the  heat  exchanged  with  the  outside  by 
V2.  To  calculate  the  order  of  magnitude  of  the 
effect  anticipated,  water  may  be  taken,  the  heat 
capacity  of  which  is  especially  large.  A  mass  of 
water,  having  at  0°  an  inertia  equal  to  1  g.,  will  have 
a  larger  inertia  at  100°.  The  difference  is  obtained 
by  dividing  the  heat  absorbed,  100  gram  degree 
calories  or  4.18  X  109  ergs,  by  F2,  which  in  the  same 
system  of  units  is  equal  to  9  X  1020,  which  gives 
about  5  X  10~12,  that  is  to  say  a  quite  imperceptible 
change. 

Nevertheless  this  example  shows  that,  from  the 
theoretical  point  of  view,  the  idea  of  mass  must  not 
any  longer  be  confused  with  that  of  quantity  of 
matter,  as  was  done  by  Newton.  Two  masses  of 
water  of  equal  inertia,  one  taken  at  100°  and  the 
other  at  0°,  do  not  contain  the  same  quantity  of 
matter,  since  they  cease  to  be  equal  when  reduced 
to  the  same  temperature;  to  put  it  differently,  two 


CHANGES    OF   MASS  87 

masses  of  water  containing  the  same  number  of 
molecules  do  not  have  the  same  inertia  unless  they 
are  taken  at  the  same  temperature,  for  then  their 
energies  are  equal. 

3.  Change  of  mass  with  velocity.-  —  The  mass  of  a 
body  depends  on  its  state  of  rest  or  of  motion  with 
respect  to  given  observers.  In  fact,  when  a  body  of 
initial  mass  m0  acquires  the  velocity  v,  its  mass 
increases  on  account  of  the  kinetic  energy  acquired 
according  to  (6)  : 


Its  total  energy  E  then  becomes 


or 

v4 
E  = 


From  this  formula  it  is  seen  that  the  quantity 
J^WoV2,  called  ordinarily  the  kinetic  energy  of  the 
moving  body,  constitutes  only  a  very  small  part  of 
the  energy  corresponding  to  the  passage  from  the 
reference  system  O0,  in  which  the  body  is  at  rest, 
to  the  system  Oi,  in  which  it  is  in  motion.  The 
quantity  of  latent  energy  mQV2  remains  hidden  to 
our  senses,  which  perceive  only  its  exceedingly  fee- 
ble variation.  This  formula  shows,  moreover,  that 
kinetic  energy  loses  its  significance  as  a  special 
form  of  energy,  which  is  inevitable,  for  if  one 
reduces  inertia  to  energy  one  may  not  in  turn  reduce 


88  PHILOSOPHY   AND   THE    NEW    PHYSICS 

part  of  energy  to  inertia.  This  is  why  all  forms 
of  energy  are  functions  of  the  velocity  and  grow 
with  it. 

4.  Change  of  mass  with  radiant  energy. — If    the 
space    comprised    within  a  material  enclosure  is 
filled  with  black  radiation  corresponding  to  a  given 
temperature,  the  mass  M  of  the  system  will  be,  by 
virtue  of  the  inertia  of  the  radiation,  larger  than 
it  would  be  without  the  latter:  this  excess  mass  is 
proportional  to  the  total  energy  of  the  radiation. 

5.  Change   of  mass   in   chemical   reactions.- — We 
have  already  seen  that  the  principle  of  the  con- 
servation  of   mass,   if   applied   to   the   individual 
masses  of  the  bodies  present  in  a  closed  system, 
is  generally  erroneous.     In  particular,  there  is  no 
conservation  of  the  mass  of  the  bodies  in  chemical 
reactions  or  in  radioactive  transmutations. 

Chemical  reactions  being  all  exothermic  or  endo- 
thermic,  it  follows  that,  by  virtue  of  the  relation 
deduced  from  (16), 

(17)  A#o  =  Aw0F2 

the  sum  of  the  masses  of  the  elements  combined  does 
not  remain  constant. 

Take,  for  example,  the  formation  of  water  start- 
ing from  its  elements  taken  in  the  gaseous  state. 
The  combination  of  2  grams  of  hydrogen  with  16 
grams  of  oxygen  sets  free  69000  gram-degree 
calories,  equivalent  to  about  3  X  10 12  ergs.  We 
would  not  obtain  18  grams  of  water,  because  the 
heat  liberated  in  the  form  of  radiation  carries  with  it 


CHANGES    OF   MASS  89 

a  loss  of  mass  equal  to  J£  X  10~8  grams,  this  being  a 
difference  of  one-fifth  of  a  billionth  (.2  X  1Q-9) 
between  the  mass  of  the  detonating  gas  and  that  of 
the  water  that  it  can  form  at  the  same  temperature. 
6.  Change  of  mass  in  radioactive  transformations. — 
The  same  will  hold  true  of  the  transformations 
of  radioactive  bodies.  The  initial  mass  of  one  of 
these  bodies  and  the  total  mass  of  its  disintegration 
products  at  the  end  of  a  certain  time  will  not  be 
equivalent,  the  transformation  being  accompanied 
by  radiation.  It  is  known  that  one  gram  of  metallic 
radium  sets  free  130  calories  per  hour  while  it  is 
transformed  into  radium  D  and  helium,  through  the 
successive  forms  of  emanation,  radium  A,  B,  C. 
Taking  into  account  the  fact  that  the  mean  life  of 
an  atom  of  radium  is  about  2600  years,  it  may  be 
computed  that  the  complete  transformation  of  one 
gram  of  radium  into  helium  and  radium  D  would 
liberate  an  energy  equal  to  1.1  X  1017  ergs.  The 
emission  of  this  energy  would  correspond  to  a 
difference  between  the  initial  mass  of  the  radium 
and  that  of  the  radium  D  and  the  helium,  equal,  per 

gram,  to 

i  i  v  in17 

A  •       ^>  1    o    vx    i  r\    4 

Am° =  -9x16*- 

The  disintegration  of  radium  into  helium  and 
radium  D  represents  merely  one  step  of  the  trans- 
formations that  start  from  uranium  and  end  with  he- 
lium and  lead.  The  complete  disintegration  of  a 
given  quantity  of  uranium  into  helium  and  lead 
would  represent  a  loss  of  mass  exceeding  one-ten- 


90  PHILOSOPHY    AND    THE    NEW    PHYSICS 

thousandth  of  the  original  uranium.  The  fraction 
of  the  mass  thus  transformed  into  radiant  energy  is  of 
an  order  of  magnitude  much  greater  than  in  the  case 
of  chemical  reactions.  It  may  be  presumed  that  it 
comes  from  the  latent  energy  of  the  uranium,  that  is, 
from  its  intra-atomic  energy.  If  we  could  succeed 
in  establishing  exactly,  to  quantities  of  the  order  of 
magnitude  10~4,  the  relation  of  the  masses  in  the 
case  of  radioactive  transformations,  it  would  be 
possible  to  verify  the  identity  of  mass  and  energy. 
To  sum  up,  energy  is  inert  and  the  mass  of  a  body 
is  equal  to  its  internal  energy  which  it  serves  to 
measure.  This  internal  energy  represents  at  the 
absolute  zero  an  enormous  accumulation  of  intra- 
atomic  energy.  According  as  a  body  acquires  or 
gives  up  energy,  its  mass  increases  or  diminishes. 
It  is  greater  when  the  body  is  in  motion  than  when 
it  is  at  rest,  greater  when  hot  than  when  cold,  when 
electrified  than  when  discharged,  it  changes  in  chem- 
ical reactions  and  in  a  more  perceptible  way  in  ra- 
dioactive transformations.  The  principle  of  the 
conservation  of  mass  formulated  by  Lavoisier  is  true 
only  as  a  first  approximation :  it  becomes  merged  in 
that  of  the  conservation  of  energy. 


CHAPTER  VI 
THE  WEIGHT  OF  ENERGY 

14.    THE     WEIGHT    OF     ENERGY;     ITS    EXPERIMENTAL 
VERIFICATIONS. 

The  experiments  of  Eotvos  show  that  if  energy 
is  inert  it  must  have  weight  in  proportion  thereto. 
If  this  were  not  so,  a  certain  quantity  of  uranium 
and  its  disintegration  products,  helium  and  lead, 
would  have  equal  weights  but  different  masses, 
and  consequently,  would  not  be  given  the  same 
acceleration  under  the  action  of  gravity.  There 
would  have  to  exist  at  one  and  the  same  spot  diff- 
erences equal  to  at  least  one-tenthousandth  in  the 
values  corresponding  to  the  acceleration  of  gravity, 
and  this  seems  to  be  capable  of  measurement. 
Thus  energy  possesses  not  only  an  inert  mass,  but  it 
possesses  also  a  ponderable  mass  /*  =  E/V2.  In 
accordance  with  what  is  true  for  inertia,  a  change  in 
internal  energy  is  accompanied  by  a  simultaneous 
change  of  mass  and  weight.  A  body  is  heavier  when 
in  motion  than  when  at  rest,  when  hot  than  when  cold, 
when  in  a  state  of  electrification  than  when  neutral, 
detonating  gas  than  the  water  it  produces,  uranium 
than  its  disintegration  products. 

Langevin1   sees   an   experimental   proof   of   the 

1  P.  Langevin,  Journal  de  Physique,  juillet  1913,  p.  584. 

91 


92  PHILOSOPHY   AND    THE    NEW    PHYSICS 

inertia  and  of  the  weight  of  internal-  energy  in  the 
departures  from  Prout's  law.  This  law  states  that 
the  atomic  weights  are  integral  multiples  of  the 
same  quantity.  While  it  is  reasonably  exact, 
nevertheless  the  weights  do  present  slight  irregulari- 
ties with  respect  to  this  law.  These  departures 
would  be  caused  by  changes  of  internal  energy 
through  emission  or  absorption  of  radiation  ac- 
companying the  formation  of  atoms  from  the  dis- 
integration of  primordial  elements,  as  seen  in 
radioactivity  or  the  inverse  process  of  integration, 
not  as  yet  observed,  with  the  formation  of  heavy 
atoms.  The  sum  of  the  weights  of  the  atoms  thus 
formed  would  differ  from  that  of  the  atoms  trans- 
formed, by  a  quantity  equal  to  the  change  in 
energy  divided  by  the  square  of  the  velocity  of 
light.  These  departures  are  such  that  the  energy 
put  into  play  would  be  of  the  same  order  of  magni- 
tude as  that  actually  observed  in  the  course  of 
radioactive  transformations.  If,  for  example,  the 
atom  of  oxygen  resulted  from  the  condensation  of 
16  atoms  of  hydrogen  or  four  atoms  of  helium,  it 
would  be  sufficient  for  an  explanation  of  the  atomic 
weight  15.87  being  less  than  16,  to  assume  that  this 
condensation  is  accompanied  by  a  loss  of  energy 
only  five  times  greater  than  that  set  free  during  the 
transformation  of  one  atom  of  radium  into  radium 
D.  The  interest  of  such  an  explanation  of  the 
departures  from  Prout's  law  is  to  make  the  hypothe- 
sis of  the  unity  of  matter  possible,  that  is,  the  hypo- 
thesis that  all  atoms  are  composed  of  one  primordial 


WEIGHT    OF    ENERGY  93 

element  or  several  such,  and  this  can  not  be  recon- 
ciled with  these  departures  so  long  as  the  principle 
of  the  conservation  of  mass  in  chemical  reactions 
is  assumed. 

Energy  possessing  a  ponderable  mass  and  the 
inertia  of  a  body  being  nothing  but  the  inertia  of 
its  internal  energy,  Newton's  law  expresses  in 
reality  the  law  of  attraction  of  energy  by  energy. 
We  shall  see  what  follows  from  this  for  free  radiation 
and  consequently  for  luminous  radiation. 

Radiation  propagated  freely  in  a  vacuum  repre- 
sents, per  unit  volume,  a  certain  energy  density  E 
and  a  certain  electromagnetic  momentum  equal 
to  E/V.  It  follows  therefrom  that  it  possesses 
an  inert  mass,  defined  as  the  momentum  divided 
by  the  velocity,  E/V2.  If  every  inert  mass  implies 
the  existence  of  a  ponderable  mass  in  proportion 
thereto,  a  light  ray  will  have  weight;  it  will  be 
attracted  by  a  mass  situated  in  its  neighborhood 
by  virtue  of  Newton's  law.  It  will  be  deviated  in  a 
gravitational  field  in  proportion  to  the  angle  be- 
tween the  direction  of  the  ray  and  that  of  the  force 
of  attraction.  Einstein1  has  calculated  the  magni- 
tude of  this  deviation  and,  in  1911,  arrived  at  the 
formula 

2KM 
a  = 


where  a  is  the  deviation  of  the  ray  passing  by  a 
spherical  mass  M  (for  example  the  mass  of  a  star), 

1  Einstein,  Ann.  der  Phys.  vol.  xxxv,  1911,  p.  898. 


94  PHILOSOPHY    AND    THE    NEW    PHYSICS 

K  the  constant  of  gravitation,  R  the  distance  from 
the  center  of  the  sphere  to  the  ray.  For  a  ray 
passing  in  the  neighborhood  of  the  surface  of  the 
Sun,  a  becomes  equal  to  .S3",  which  constitutes  a 
quantity  that  can  be  measured,  by  observing,  for 
example,  the  position  of  a  star  near  the  edge  of  the 
Sun  at  the  instant  of  a  total  eclipse. 

By  virtue  of  Einstein's  equivalence  principle, 
luminous  radiation  in  the  interior  of  a  system  that 
undergoes  an  acceleration  must  behave  like  a  pro- 
jectile; instead  of  describing  a  straight  line  it  will 
describe  a  parabola.  Observers  enclosed  in  Jules 
Verne's  cannon  ball,  which  would  fall  with  accelera- 
tion, could  therefore  by  the  aid  of  optical  experi- 
ments detect  the  state  of  acceleration  of  the  system, 
without  otherwise  knowing  whether  they  should 
attribute  it  to  the  presence  of  a  gravitational  field 
or  to  the  state  of  acceleration  of  their  cannon  ball. 

The  equivalence  between  the  inert  mass  and 
the  ponderable  mass  carries  with  it  the  equiva- 
lence of  the  effects  produced  on  physical  phenomena 
by  a  field  of  gravitation  and  those  due  to  a  suitable 
state  of  acceleration  of  the  reference  system  to  which 
they  are  referred.  It  must  follow  therefrom  that  the 
potential  of  gravitation  acts  on  the  passage  of  time 
and  the  dimensions  of  bodies  in  the  same  manner  as 
acceleration.  Now  it  follows  from  the  Lorentz 
group  that  a  body  is  the  more  contracted  in  the 
direction  of  its  translation  for  observers  00  who  see 
it  pass  and  that  the  velocity  of  the  phenomena  that 
take  place  in  it,  measured  by  these  same  observers, 


WEIGHT    OF    ENERGY  95 

is  the  more  retarded,  in  proportion  as  its  velocity  is 
more  accelerated  relatively  to  them.  In  the  same 
way,  a  body  will  be  the  more  contracted  and  the 
march  of  the  phenomena,  of  which  it  is  the  seat,  the 
more  retarded,  in  proportion  as  the  potential  of  gravi- 
tation of  the  place  where  it  is  found  is  increased. 
Two  equal  chronometers  placed  at  unequal  distances 
from  the  Sun  will  go  at  different  rates,  and  the 
more  distant  one  will  run  ahead  of  the  nearer.  Now 
a  chemically  defined  molecule  that,  by  virtue  of  its 
oscillations,  emits  a  given  spectral  light  constitutes 
a  chronometer  of  atomic  dimensions.  If,  therefore 
two  identical  molecules  at  positions  of  different 
gravitational  potential  are  observed  with  the  aid 
of  a  spectroscope,  one  on  the  surface  of  the  Sun 
and  the  other  on  the  surface  of  the  Earth,  the  os- 
cillations of  the  second  being  more  rapid  than  those 
of  the  first  and  consequently  the  frequency  of  the 
light  that  it  emits  being  greater,  it  ought  to  be 
found  that  the  ray  emitted  by  the  second  is  displaced 
in  the  spectrum,  with  respect  to  the  ray  emitted  by 
the  first,  in  the  direction  of  the  violet.  Knowing 
the  difference  of  the  potential  of  gravitation  at  the 
surface  of  the  Sun  and  at  the  surface  of  the  Earth, 
it  is  easy  to  calculate  that  the  difference  in  the  wave 
lengths  of  the  spectral  rays  ought  to  reach  about 
Koo  Angstrom  unit,  that  is,  one-millionth  of  a 
micron,  which  is  a  quantity  accessible  to  experiment. 
It  is  remarkable  that  displacements  of  this  order 
have  actually  been  observed  by  Fabry  and  Buisson 
by  comparing  the  Fraunhofer  rays  of  the  solar 


96  PHILOSOPHY    AND    THE    NEW    PHYSICS 

spectrum  with   the   corresponding  rays   of   a   ter- 
restrial source.1 

15.  THE  GENERALIZED  PRINCIPLE  OF  RELATIVITY 
AND  ELNSTEIN'S  THEORY  OF  GRAVITATION. 

The  relation  /*  =  E/V2  shows  that  the  laws  of 
the  conservation  of  weight  are  the  same  as  those 
of  the  conservation  of  energy.  Now  the  weight  of 
a  body  in  a  gravitational  field  changes  when  it  is 
displaced  in  the  field:  it  increases  when  the  body 
is  raised.  To  this  increase  in  weight  there  must 
be  a  corresponding  increase  in  energy  equivalent, 
to  the  work  expended  against  the  weight  in  raising 
the  body.  This  change  of  energy  carries  with  it, 
in  virtue  of  the  formula  M  —  E/V2,  either  a  change 
of  mass  or  a  change  ^of  the  velocity  of  light  in  the 
gravitational  field  at  the  point  considered.  This 
is  the  starting  point  of  the  new  theories  of  gravi- 
tation according  to  the  relativistic  ideas. 

G.  Mie2  has  developed  a  theory  in  which  he 
,  makes  the  mass  but  not  the  velocity  of  light  depend 
on  the  potential  of  gravitation.  He  thus  safe- 
guards the  postulate  of  the  constancy  of  the  veloci- 
ty of  light  required  by  the  relativity  principle, 
but  he  is  obliged  to  renounce  the  equivalence  be- 
tween ponderable  mass  and  inert  mass  established 
by  Eotvos.  G.  Nordstrom3  has  sought  to  maintain 

1  Cf.  Freundlich,  Phys.  Zeitschr.  vol.  xv,  1914,  p.  369. 

2  G.  Mie,  Ann.  der  Phys.,  vol.  xc,  1913,  p.  25;  Phys.  Zeitschr., 
1914,  p.  115  and  169. 

3G.  Nordstrom,  Phys.  Zeitschr.,  1912,  p.  1126;  1914,  p.  375, 
604;  Ann.  der  Phys.,  1913,  p.  533,  856;  1914,  p.  1101. 


THEORY    OF    GRAVITATION  97 

the  postulate  of  the  constancy  of  the  velocity  of 
light  and  the  proportionality  between  ponderable 
mass  and  inert  mass  over  the  widest  range,  but  he 
is  compelled  to  assume  a  change  in  the  length  of 
bodies  and  in  the  rate  of  phenomena,  as  a  function 
of  the  potential  of  gravitation,  which  does  not  agree 
with  that  predicted  by  the  Lorentz  group.  Einstein 
also  has  resigned  himself  to  abandoning  the  con- 
stancy of  the  velocity  of  light  in  a  field  with  varying 
potential  and  to  assuming  that  it  varies  with  posi- 
tion according  to  the  formula 

(19)  V  m  70(l  +  Y 

where  <j>  represents  the  magnitude  of  the  Newtonian 
potential  at  the  point  considered.  The  Lorentz 
group  is  then  applicable  only  to  regions  where  the 
potential  of  gravitation  is  constant,  or,  what  in 
virtue  of  the  equivalence  principle  comes  to  the 
same  thing,  to  systems  in  uniform  translatory 
motion. 

Einstein1  has  sought  a  group  of  transforma- 
tions, having  that  of  Lorentz  as  a  special  case, 
and  such  that  the  equations  of  the  field  of  gravi- 
tation can  be  reduced  to  the  form  that  those  of  a 
system  without  gravitation  have,  when  referred  to 
a  reference  system  in  a  state  of  acceleration.  The 
discovery  of  this  group,  for  which  he  was  indebted 
to  the  absolute  differential  calculus,  created  by 

1  Einstein,  Die  formalen  Grundlagen  der  allgemeinen  Relativi- 
tats  theorie  (Ber.  Berl.  Ak.,  vol.  XLI,  1914,  p.  1030). 

7 


98  PHILOSOPHY    AND    THE    NEW    PHYSICS 

Christoffel  and  developed  by  Ricci  and  Levi-Civita, 
has  enabled  him  to  generalize  the  relativity  prin- 
ciple by  extending  it  to  any  arbitrary  motion  of 
the  reference  axes  whatever,  thus  bridging  the  fol- 
lowing serious  epistemological  gap,  pointed  out  by 
Mach. 

Psycho-physiology  teaches  us  that  our  senses 
make  known  to  us  only  relative  states  and  changes 
of  bodies,  without  ever  revealing  to  us  any  absolute 
state  or  change.  Thus  our  sight  does  not  reveal 
to  us  the  absolute  shape  and  dimensions  of  a  body, 
but  simply  the  fact  that  a  figure  has  such  a  shape 
and  such  a  size  relatively  to  another  taken  as  com- 
parison term,  this  purely  relative  shape  and  size 
not  being  altered  in  any  dilatation  or  any  continu- 
ous transformation  whatever  of  the  universe.  In 
the  same  way,  we  do  not  perceive  Newton's  absolute 
space,  to  which  we  might  refer  all  moving  objects, 
but  merely  the  relative  state  of  rest  or  motion  of 
bodies.  Similarly  our  thermal  sensibility  does 
not  teach  us  anything  about  the  absolute  tempera- 
ture of  bodies,  but  only  about  the  changes  in  the 
states  of  affairs  as  regards  heat  losses  between  our 
skin  and  the  surrounding  medium.  If,  therefore, 
we  wish  to  confine  ourselves  to  the  data  of  sense 
perception,  we  must  not  in  natural  philosophy 
speak  of  absolute  velocity,  acceleration  or  inertia. 

Classical  mechanics  does  not  satisfy  this  require- 
ment. It  succeeds  in  preserving  the  relativity  of 
velocities,^but  it  concedes  an  absolute  sense  to  the 
idea  of  acceleration  and  to  that  of  inertia,  con- 


GENERALIZED    RELATIVITY  90 

sidered  as  capacity  of  resistance  to  acceleration  of 
a  body.  According  to  these  principles  the  motion 
of  two  masses  isolated  in  space  and  sufficiently 
close  to  be  able  to  exert  actions  on  each  other, 
would  be  governed  by  Newton's  law  of  attraction, 
independently  of  the  system  of  fixed  stars  to  which 
it  is  referred;  for:  "It  would  be,"  says  Euler,  "a 
very  strange  proposition  and  contrary  to  a  host  of 
other  dogmas  of  metaphysics,  to  say  that  the 
fixed  stars  influence  the  inertia  of  bodies."1  But, 
in  fact,  we  perceive  merely  relative  distances  of 
bodies:  hence  we  can  only  observe  and  define  the 
relative  velocities  and  accelerations  of  bodies, 
that  is  to  say,  the  first  and  second  derivatives 
of  their  distances.  Consequently  the  inertia  of 
a  body  can  only  be  defined  as  its  resistance  to  the 
relative  accelerations  which  it  experiences  with 
respect  to  other  bodies  that  do  not  participate  in 
its  state  of  motion.  The  inert  mass  of  a  body 
appears,  therefore,  as  a  relative  quantity,  which 
depends  on  the  distribution  of  the  masses  about 
this  body  and  on  their  state  of  rest  or  motion  with 
respect  to  it:  it  will  be  greater,  the  greater  the 
number  of  other  masses  in  its  neighborhood,  which 
do  not  participate  in  its  state  of  acceleration; 
it  will  disappear  in  the  opposite  case.  A  body 
is  inert  because  it  is  surrounded  by  other  bodies. 
Its  inertia  results  from  the  mean  action  of  all 
masses  distributed  in  the  universe,  so  that,  con- 
trary to  Euler's  assertion,  the  fixed  stars  do  deter- 

1  Euler,  Reflexions  sur  1'espace  et  le  temps,  p.  328. 


100  PHILOSOPHY    AND    THE    NEW    PHYSICS 

mine  in  part  the  inertia  and  the  motion  of  the 
Earth.  The  principle  of  inertia  thus  loses  all 
absolute  sense:  it  becomes  a  relative  and  statistical 
principle. 

To  put  our  physical  conceptions  into  accord  with 
the  data  of  our  sense  perception,  and  to  set  natur- 
al philosophy  free  from  metaphysical  entities  that 
encumber  it,  such  as  the  ideas  of  absolute  space 
and  privileged  axes,  it  is  desirable  to  state  the  laws 
of  physics  in  an  intrinsic  language,  independent 
of  any  reference  system,  just  as  Euclid's  geometry 
as  compared  with  Descartes'  is  an  intrinsic  language 
free  of  the  consideration  of  coordinates.  For  this 
purpose  it  does  not  suffice  to  make  the  form  of  the 
physical  laws  independent  of  the  state  of  uniform 
translation  of  the  coordinate  axes;  it  must  be  made 
independent  of  any  motion  whatever  of  these  axes; 
or,  in  Minkowski's  geometrical  language,  it  must 
be  possible  to  refer  them  in  four  dimensional  space 
to  a  system  of  oblique  axes  or  a  system  of  curvi- 
linear coordinates,  as  well  as  to  a  rectangular  system 
formed  by  rectangular  coordinates. 

Einstein's  will  be  the  glory  of  having  succeeded 
in  satisfying  this  last  condition,  by  giving  to  the 
physical  laws  a  universally  invariant  form,  or,  as 
we  say  nowadays,  co variant  for  any  change  of  coordi- 
nate axes.  To  accomplish  this  generalization  of 
the  relativity  principle,  Einstein  started  from  the 
equivalence  principle,  deduced  by  him  from  Eotvos' 
experiments  on  the  strict  proportionality  of  the  inert 
mass  and  the  gravitational  mass  of  bodies,  which 


GENERALIZED    RELATmiS:  101 


states  the  impossibility  of  distinguishing  the  effects 
of  a  field  of  gravitation  from  those  of  a  field  of  mo- 
tion. The  effects  produced  by  a  field  of  gravitation 
can  always  be  interpreted  by  a  state  of  acceleration 
of  a  body  removed  from  any  field  of  force,  and  con- 
versely. From  this  it  follows  that  the  existence  of 
a  field  of  gravitation  in  empty  space  is  purely  re- 
lative; it  depends  on  the  problem,  insoluble  by  ex- 
periment, of  finding  whether  the  system  from  which 
it  is  observed  is  at  rest  or  in  accelerated  motion; 
the  real  field  for  a  system  considered  at  rest  will  be 
fictitious  for  other  systems  in  motion  which  the  gen- 
eralized relativity  principle  declares  equivalent 
to  the  first.  Einstein  then  shows  that  the  form  of 
the  physical  laws  may  be  rendered  independent  of 
any  system  of  privileged  axes,  provided  the  quanti- 
ties characteristic  of  the  field  of  gravitation  are 
made  to  appear  in  the  physical  laws;  or,  more  pre- 
cisely, provided  these  laws  be  considered  as  relations 
between  the  quantities  characteristic  of  material 
phenomena  and  the  quantities  characteristic  of  the 
field  of  gravitation,  these  quantities  being  tensors, 
and  matter  designating  everything  that  is  super- 
imposed on  the  field  of  gravitation.  These  rela- 
tions, being  invariant  for  every  transformation  of 
the  reference  system,  are  intrinsic  equations,  ex- 
pressed with  the  aid  of  tensor  equalities,  from  which 
every  coordinate  system  has  disappeared. 

This  theory  involves  remarkable  consequences. 

It  appears  at  first  as  a  universal  relativism  ex- 
pressed with  the  aid  of  an  absolute  calculus.  The 


102  I'HJLOSOPHi'    AND    THE    NEW    PHYSICS 

metrical  properties  of  space,  the  kinematical  and 
dynamical  properties  of  mechanical  systems,  the 
physical  properties  of  any  region  whatever  of  space 
vary  according  to  the  point  of  view  of  the  observer. 
These  properties  depend,  in  fact,  on  the  field  of 
gravitation  and  the  state  of  motion  of  the  system 
from  which  they  are  observed. 

The  influence  of  gravitation  is  exerted  on  every 
physical  process,  on  all  matter  including  the  electro- 
magnetic and  luminous  field.  Conversely,  it  has 
its  origin  in  every  region  of  the  universe  where  the 
material  tensor  is  different  from  zero.  Since  the 
material  tensor  corresponds  to  a  reality,  gravitation 
also  involves  a  real  element  with  which  a  fictitious 
field  of  gravitation,  equivalent  to  an  arbitrary 
motion  in  empty  space,  may  always  be 'combined. 

Empty  space  is  not  the  absolute  and  infinite 
void  of  Newton's  followers:  it  is  the  pure  field  of 
gravitation  on  which  no  matter  is  superimposed. 
From  the  physical  point  of  view  there  is  no  amor- 
phous void,  endowed  with  pure  receptivity,  in 
which  material  points  could  be  imagined,  attract- 
ing or  repelling  one  another  according  to  certain 
laws,  like  Newton's  law,  and  thus  communicating 
absolute  accelerations  to  one  another.  We  can  not 
speak  of  empty  space,  except  where  there  is  a  field 
of  gravitation,  not  merely  coexistent  with  this 
space,  but  veritably  the  creator  of  space,  of  its 
metrical  properties,  and,  we  may  say,  its  extent. 
The  world  must  be  thought  of  no  more  as  an  as- 
semblage of  bodies  lost  in  an  infinite  void,  but  as 


GENERALIZED    RELATIVITY  103 

systems  of  bodies  and  of  electromagnetic  or  lumin- 
ous fields,  superimposed  on  gravitational  fields  of 
finite  dimensions.  The  absolute,  void,  amorphous, 
and  infinite  space  of  Newton  vanishes  like  other  idola 
fori;  and  Kant's  antinomies  advanced  in  regard  to  it 
are  abolished  as  referring  to  a  pseudo-problem. 

To  fathom  the  meaning  of  this  universal  rela- 
tivism, it  will  be  well,  at  this  stage,  to  contrast 
the  ideas  of  Einstein  and  those  of  Lorentz. 

For  Einstein  there  is  no  infinite  void,  no  motion- 
less ether,  no  uniform  course  of  time,  and  conse- 
quently there  are  no  privileged  reference  systems 
and  clocks;  there  is  no  region  of  space  enjoying 
absolute  physical  properties.  The  Lorentz  con- 
traction is  not  true  in  the  sense  that  it  corresponds 
to  an  absolute  deformation,  a  body  not  having  any 
shape  except  relatively  to  another.  It  is  a  recipro- 
cal semblance  of  reality,  arising  from  local  time, 
from  the  fact  that  the  clocks  of  observers  connected 
with  one  body  and  those  of  observers  in  motion 
with  respect  to  it,  do  not  go  at  the  same  rate. 
The  distinction  between  reality  and  semblance 
vanishes:  there  are  only  relative  truths,  science 
being  unable  to  establish  anything  but  comparisons, 
by  ascertaining  coincidences  and  by  comparing 
colors  (frequencies  of  radiating  sources  serving  as 
clocks).  The  only  absolute  reality  that  it  can 
attain  consists  of  the  laws  of  physical  phenomena, 
expressed  by  intrinsic  equations  by  the  aid  of  tensor 
equalities,  the  form  of  which  is  independent  of 
every  system  of  space  and  time  coordinates.  If 


104  PHILOSOPHY   AND    THE    NEW    PHYSICS 

God  exists  and  it  should  please  him  to  recount  the 
history  of  the  world  in  the  extrinsic  and  artificial 
language  of  time  and  space,  it  would  be  merely  by 
an  arbitrary  decree  of  his  free  will  in  a  complete  state 
of  intellectual  indifference  that  would  make  him 
choose,  once  for  all,  a  system  of  space  coordinates 
and  a  clock  (that  is,  a  radiating  source  connected 
with  this  system  and  consequently  regarded  as  at 
rest).  Having  thus  fixed  arbitrarily  the  meaning 
of  simultaneity  and  order  of  sequence  of  events,  he 
could  establish  their  universal  chronology. 

The  ordinary  distinction  between  semblance 
and  reality  would,  on  the  contrary,  exist  for  an 
infinite  intelligence,  if  there  be,  as  Lorentz  is  in- 
clined to  believe,  an  ether  which  is  motionless 
but  otherwise  of  a  nature  unknown  to  us,  but  it 
would  be  very  different  from  the  mechanical  ether 
of  Faraday,  Lord  Kelvin,  and  Sir  Oliver  Lodge. 
There  would,  therefore,  be  for  an  omniscient  intelli- 
gence a  privileged  reference  system  and  clock, 
whatever  the  system  of  axes,  provided  it  be  con- 
nected with  the  ether,  and  whatever  the  clock  at 
rest,  provided  it  be  free  from  the  influence  of 
gravitation.  This  omniscient  mind  could  with 
propriety  speak  of  absolute  motion,  order  of  succes- 
sion, and  synchronism.  The  Lorentz  contraction 
and  the  retardation  of  clocks  would  appear  to  him 
as  physical  phenomena,  due  to  the  connections 
between  matter  and  ether,  by  which  an  action  is 
exerted  by  the  latter  on  the  former.  But  this 
privileged  set  of  three  reference  axes  and  this  course 


GENERALIZED    RELATIVITY  105 

of  absolute  time  would  be  concealed  from  us  forever 
as  a  consequence  of  the  same  action  of  the  ether  on 
the  bodies,  which  would  be  precisely  such  as  to 
prevent  us  from  discovering  their  absolute  motion. 
The  observers  00  would  have  no  better  ground  for 
saying  they  were  at  rest  and  recording  true  time 
than  the  observers  Oi.  Any  experimenter  whatever 
could  always  explain  what  he  observes  by  supposing 
either  that  he  is  at  rest  in  the  ether  or  that  his 
laboratory  is  traversed  by  an  ether  current  which 
produces  the  effect  of  shortening  his  instruments 
and  retarding  his  clocks,  or  that  there  is  no  ether  at 
all  but  it  is  the  motion  of  a  rod  or  a  clock  in  his 
laboratory  that  produces  the  shortening  of  the  one 
and  the  retardation  of  the  other. 

According  to  the  pragmatist  theory  of  truth 
the  two  concepts,  that  of  Einstein  and  that  of  Lo- 
rentz,  are  equivalent,  since  they  are  equally  in 
accord  with  phenomena. 

On  one  hand,  Einstein's  concept,  being  in  accord 
with  the  data  of  psycho-physiology,  by  respecting 
the  conditions  of  knowledge  imposed  by  our  sense 
perceptions,  by  practising  the  scholastic  adage 
non  sunt  multiplicanda  entia  sine  causa,  by  reliev- 
ing physics  of  metaphysical  entities  that  encumber 
it,  by  delivering  us  from  a  swarm  of  pseudo-prob- 
lems, is  strictly  positive,  more  economic  than  that  of 
Lorentz,  and  unassailable  in  itself;  on  the  other 
hand,  that  of  Lorentz,  by  maintaining  the  ether, 
safeguards  our  old  habits  of  thought,  satisfies  our 
craving  for  the  absolute,  sets  our  minds  at  rest, 


106  PHILOSOPHY    AND    THE    NEW    PHYSICS 

establishes  a  bond  of  union  between  the  physics  of 
yesterday  and  that  of  today,  and  falls  into  the 
category  of  explanatory  theories,  since  the  shorten- 
ing of  bodies,  the  retardation  of  clocks,  the  con- 
stancy of  the  velocity  of  light  in  a  gravitational  field 
of  constant  potential  are  explained  by  the  connec- 
tions of  matter  and  ether.  But  the  existence  of 
the  ether  is  forever  rendered  problematic  by  virtue 
of  the  relativity  principle.  Its  nature  is  unknown 
to  us,  since  the  mechanical  properties  with  which 
Faraday,  Helmholtz,  Lord  Kelvin,  Sir  Oliver  Lodge 
endowed  it  have  already  condemned  it.  It  does  not 
seem  to  represent  necessarily  the  anticipation  of 
future  observations  and  experiments,  like  Pasteur's 
theory  of  microbes  or  the  atomic  theory;  it  is  merely 
a  method  of  exposition,  a  figurative  hypothesis  to 
uphold  the  spirit  of  abstraction,  which,  useful  for 
the  minds  that  Duhem  called  broad  and  weak,  be- 
comes superfluous,  cumbersome  and  tiresome  for  the 
minds  that  he  names  narrow  but  profound. 

Whatever  the  outcome  may  be,  Einstein's  re- 
sults as  to  inertia,  the  weight  of  energy,  and  the 
relativity  of  phenomena  seem  permanent  acquisi- 
tions. The  relativity  principle  represents  one  of  the 
norms  of  physical  research  which  limits  the  field  of 
our  investigations  and  determines,  in  part,  the  form 
of  the  equations  of  physics. 

16.    ASTRONOMICAL  VERIFICATION. 

The  philosophical  importance  presented  by  Ein- 
stein's theory  of  gravitation,  based  on  the  general- 


ASTRONOMICAL   VERIFICATION  107 

ized  relativity  principle,  should  not  lead  us  to  forget 
the  interest  attached  to  its  practical  results,  the 
most  sensational  of  which,  independently  of  those 
already  indicated,  is  the  calculation  of  the  secular 
anomaly  of  the  perihelion  of  Mercury.1 

To  account  for  it,  Tisserand,2  as  is  well  known, 
proposed  to  replace  Newton's  law  by  a  more  general 
formula,  similar  to  Weber's  electrodynamical  law. 
Of  all  the  theories  proposed  since,  none  satisfies  the 
mind  like  Einstein's  theory  of  gravitation. 

According  to  this  theory,  there  exists  no  absolute 
invariant  appertaining  to  a  material  point,  that  is, 
the  exact  equivalent  of  inert  mass  or  of  gravitational 
mass  in  classical  mechanics.  We  have  here  to  do 
with  a  tensorial  theory  in  which  the  numbers  Gab, 
characteristic  of  the  field  of  gravitation,  and  the 
numbers  Tab,  characteristic  of  the  field  of  inertia 
(ordinary  matter  and  electromagnetic  field),  form  a 
covariant  tensor.  It  is  possible  to  attach  to  these 
tensors  two  relative  scalar  invariants,  G  and  T, 
which  may,  if  desired,  be  considered  by  extension  as 
measures  of  a  gravitational  mass  and  an  inert  mass. 

Let  us  now  consider  what  follows  from  this,  tak- 
ing account  of  the  inertia  of  energy,  in  the  case  of  the 
attraction  of  Mercury  by  the  Sun. 

In  the  study  of  the  motion  of  a  material  point 
attracted  by  gravitational  masses,  a  quite  natural 
simplification  consists  in  treating  of  this  point  as  "a 

1  Einstein,  Erklarung   der  Perihelbewegung  des  Merkur   (Ber. 
Berl.  Ak.,  vol.  xlvii,  1915,  p.  830). 

2  Tisserand,  Traite  de  Mecanique  celeste,  vol.  IV,  p.  500. 


108  PHILOSOPHY    AND  THE    NEW    PHYSICS 

test  body"  placed  in  a  field  of  gravitation  due  to 
other  masses  and  not  modifying  perceptibly  the 
field  of  gravitation  of  these  masses.  Given  two 
bodies,  an  attracting  body  and  an  attracted  body, 
the  inert  mass  of  the  attracting  body  (and  the  same 
holds  for  the  attracted  body)  is  increased  in  pro- 
portion with  the  increase  of  the  potential  of  gravi- 
tation due  to  other  masses.  Now  the  Sun,  con- 
sidered as  an  attracting  mass  occupying  a  sphere  of 
radius  a,  is  surrounded  with  a  field  of  gravitation,  so 
that  it  is  immersed  in  gravitational  energy.  This 
energy,  always  positive  so  far  as  concerns  physical 
reality,  is  negative  in  the  sense  that  in  order  to 
produce  an  attracting  mass  by  condensation  of  ele- 
ments coming  from  infinity,  negative  work  must  be 
expended.  It  results  from  this  that  there  is  less 
energy  in  the  neighborhood  of  an  attracting  mass 
than  in  the  absence  of  all  mass.  If,  therefore, 
we  attribute  inertia  to  the  energy  of  gravitation, 
as  to  all  the  other  forms  of  energy,  it  follows  that, 
for  a  point  situated  at  a  very  great  distance  from  the 
Sun,  the  mass  of  the  latter  will  be 

M  =  Mo  -  AMo, 

AM0  representing  the  correction  term  due  to  the  in- 
ertia of  the  total  field  of  gravitation.  For  a  point 
situated  on  the  orbit  of  Mercury  the  effective  solar 
mass  will  be  equal  to 

M  +  AM, 

if  we  denote  by  AAf  the  supplementary  mass  due  to 
the  inertia  of  gravitation  outside  of  the  orbit  of 
Mercury.  It  will  thus  be  larger  than  the  principal 
mass  M. 


ASTRONOMICAL  VERIFICATION  109 

Taking  account  of  these  corrections,  it  is  found 
that  the  elliptical  motion  is  transformed  into  a 
pseudo-elliptic  motion  with  a  progressive  advance  of 
the  perihelion.  Applied  to  the  case  of  the  planet 
Mercury,  the  calculation  indicates  a  secular  motion 
of  the  perihelion  equal  to  43".  Since  the  observa- 
tions give  45",  this  aggreement  must  be  regarded  as 
the  more  remarkable,  because  it  is  obtained,  with- 
out any  supplementary  hypothesis,  by  the  applica- 
tion and  simplification  of  the  general  equations 
furnished  by  the  theory. 

A  hardly  less  remarkable  confirmation  of  the  theory  of  inertia 
of  energy  and  of  Einstein's  theory  of  gravitation  is  obtained  from 
the  deviation  of  light  rays  in  the  neighborhood  of  the  Sun.  On 
account  of  both  the  Newtonian  attraction  exerted  by  the  Sun  on  a 
light  ray  propagated  in  its  neighborhood  and  of  the  curvature 
of  space  produced  by  the  mass  of  the  Sun  according  to  Einstein's 
gravitational  equations,  the  path  of  the  ray  should  not  be  recti- 
linear but  curved  towards  the  center  of  attraction,  with  a  total 
deviation  given  by  the  expression 

4KM 


whic,h  is  just  twice  the  value  given  by  equation  (18),  p.  93.  In 
consequence  of  this  it  is  possible  to  predict  that  a  star  seen  near 
the  Sun  should  suffer  an  outward  deviation  equal  to  1.74"  and 
varying  inversely  as  the  distance  from  the  center  of  the  Sun  for 
the  more  distant  stars,  as  compared  with  the  position  that  it 
occupies  on  the  celestial  sphere  in  the  absence  of  the  Sun,  since 
the  star  is  seen  in  the  line  of  its  ray,  i.e.,  in  the  direction  of  the 
tangent  to  the  path  of  the  ray.  This  deduction  has  been  success- 
fully verified  by  photographing  the  same  region  of  the  sky  in  the 
absence  of  the  Sun  and  during  a  total  solar  eclipse.  The  negatives 
obtained  by  the  two  British  expeditions  undertaken  for  this  purpose 
in  the  zone  of  the  total  solar  eclipse  of  May  29,  1919,  have  given 
a  mean  deviation  of  1.79"  +  .03".  This  agrees  remarkably  well 
with  the  value  predicted  by  Einstein. 


CHAPTER  VII 
'  THE  STRUCTURE  OF  ENERGY 

17.  THE  SUCCESS  OF  THE  ELECTRONIC  THEORY; 
THE  EXPLANATION  OF  THE  RELATIONS  OF 
MATTER  AND  RADIATION. 

We  have  just  seen  that  a  body  is  inert  and  has 
weight  in  proportion  to  the  energy  it  contains, 
so  that  the  concept  of  matter  is  subsumed  under 
the  more  general  one  of  energy,  and  that  the  princi- 
ple of  the  conservation  of  mass  becomes  merged  in 
that  of  the  conservation  of  energy.  Energy,  as 
Ostwald  would  have  it,  becomes  the  only  existing 
reality,  into  which  are  absorbed  the  ether  and  the 
numerous  imponderable  agents  to  which  the  physics 
of  the  beginning  of  the  nineteenth  century  was 
partial.  Nevertheless  it  appears  that  energy  pre- 
sents itself  essentially  in  a  double  aspect:  in  the 
form  of  resinous  (negative)  electricity  endowed  with 
a  corpuscular  structure  and  in  the  form  of  free 
radiation.  In  its  first  aspect  it  is  made  up  of 
grains  of  electricity,  capable  of  moving  with  veloci- 
ties ranging  from  0  to  7,  its  aggregates  constituting 
atomic  and  molecular  structures,  relatively  stable 
and  with  astonishing  vacant  spaces,  and  appearing 
to  our  senses  in  the  form  of  continuous  bodies.  In 
its  second  aspect  it  appears  as  made  up  of  transverse 

no 


ELECTRONIC    THEORY  HI 

waves,  infinitely  expansible  and  divisible,  sweeping 
through  all  space  with  the  uniform  velocity  of  light. 
In  the  first  case  it  takes  the  name  of  matter;  in  the 
second  that  of  radiant  energy. 

The  specific  character  of  a  portion  of  matter  must 
no  longer  be  sought  in  its  mass  and  its  weight, 
since  radiant  energy  is  likewise  inert  and  endowed 
with  weight,  and  mass  is  no  longer  an  invariable 
scalar  quantity,  but  takes  the  character  of  a  tensorial 
quantity,  which  is  unsymmetric  and  variable  as  a 
function  of  the  velocity  and  the  internal  energy  of 
bodies.  That  character  must  be  sought  in  the 
number  and  nature  of  the  primordial  elements 
which  constitute  matter. 

These  elements,  revealed  in  atomic  changes  be- 
yond the  domain  of  chemistry,  are  the  electrons  and 
the  positive  remainders,  the  latter  having  a  struc- 
ture as  yet  unknown  and  presented  to  us  in  the  form 
of  the  positive  kernels  of  helium  atoms.  These 
elements  alone  remain  invariable  throughout  the 
changes  that  matter  undergoes  and  can  serve  to 
define  it. 

What  are  the  relations  between  matter  thus 
characterized  and  radiation,  and  what  is  the 
mechanism  of  their  exchanges  of  energy?  It  was 
on  this  point  that  the  metaphysical  pseudo-problem 
of  the  action  of  imponderable  on  ponderable  arose, 
and  it  is  to  it  that  the  electronic  theory  of  matter 
claims  to  give  a  satisfactory  answer. 

Let  us,  for  this  purpose,  consider  again  the  case 
of  a  charged  particle  in  quasi-stationary  motion 


112  PHILOSOPHY   AND   THE    NEW   PHYSICS 

and  let  us  see  what  happens  when  it  undergoes  an 
acceleration. 

The  wave  system  of  the  particle  in  quasi-station- 
ary motion  is  formed  by  the  system  of  radial 
electric  lines  of  force  and  of  circular  magnetic 
lines  of  force  that  it  carries  with  it.  It  may  be, 
moreover,  considered  as  the  aggregate  of  the 
electromagnetic  waves  of  velocity,  emitted  at  differ- 
ent instants  in  its  course,  and  centered  on  its  former 
positions,  which  envelop  one  another,  so  that  the 
electromagnetic  field  produced  by  the  displacement 
of  the  particle  is  determined,  not  by  the  instantane- 
ous state  of  the  particle,  but  by  all  its  former  states. 
The  energy  of  the  field  thus  created  is  localized 
nearly  entirely  in  the  immediate  neighborhood  of 
the  particle,  because  the  intensity  of  the  field  varies 
inversely  as  the  square  of  the  distance,  and  rapidly 
approaches  zero  as  the  distance  from  the  particle 
becomes  greater.  The  waves  of  velocity  which 
constitute  the  wave  system  of  an  electron  do  not 
correspond  to  any  energy  radiated  to  a  great  dis- 
tance, since  they  vanish  at  infinity.  They  represent 
kinetic  energy  which  accompanies  the  electron  in 
its  displacement,  preserving  for  a  constant  velocity 
a  fixed  distribution  around  it.  As  space  exerts^no 
viscous  action,  no  external  influence  is  requiredj  to 
conserve  this  energy  in  motion,  and  the  projected 
electron  moves  indefinitely  with  the  same  velocity 
in  conformity  with  the  principle  of  inertia,  so  long 
as  no  external  cause  modifies  its  state  of  motion 
and  produces  acceleration. 


ELECTRONIC   THEORY  113 

Let  us  examine  what  happens  in  the  latter  case. 
In  the  first  place,  the  magnetic  energy  of  the 

e2 
wave  system,  in  conformity  with  the  relation  ^-  v2 

ott 

which  is  valid  for  small  velocities,  increases  or 
diminishes  by  a  quantity  called  energy  of  change, 
which  corresponds  to  a  reorganization  of  the  lines 
of  force  of  the  wave  system.  In  the  second  place 
the  change  of  velocity  determines  the  appearance 
of  a  spherical  wave  of  acceleration,  the  radius  of 
which  increases  with  the  velocity  of  light  and  which 
remains  centered  about  the  point  where  the  electron 
was  at  the  instant  of  the  emission.  This  wave 
corresponds  at  every  point  to  the  passage  of  an 
electric  field  and  of  a  magnetic  field,  situated  in 
the  plane  tangent  to  the  wave  and  perpendicular 
to  each  other  in  this  plane.  These  fields  represent 
a  localization  of  electric  and  magnetic  energy  equal 
per  unit  volume,  and  this  has  the  effect  of  giving  to 
the  wave  of  acceleration  all  the  characteristics  of 
free  radiation. 

The  fields  present  in  the  wave  of  acceleration 
are  superimposed  on  those  of  the  velocity  waves. 
Since  the  latter,  varying  inversely  as  the  square 
of  the  distance,  diminish  much  more  rapidly  than 
the  former,  which  vary  simply  inversely  as  the 
distance,  at  a  sufficient  distance  from  the  electron 
only  the  acceleration  wave  will  exist.  The  energy 
thus  radiated  to  infinity  with  the  velocity  of  light, 
by  the  radiation  which  the  electron  emits  during 
the  time  dt,  is  proportional  to  the  square  of  the 


114  PHILOSOPHY   AND   THE    NEW   PHYSICS 

charge    and    the    acceleration    according    to    the 
relation  : 

9    /p2-,2 

(20)  \  *±  dt 

where,  in  E.  M.  U.,  v  denotes  the  acceleration  and 
V  the  velocity  of  light. 

This  radiated  energy  represents  the  intrinsic 
energy  of  the  acceleration  wave.  It  is  borrowed 
from  the  external  actions  which  modify  the  velocity 
of  the  electron.  But  it  represents  only  a  small 
part  of  the  energy  which  the  acceleration  wave  car- 
ries at  the  start  when  leaving  the  center.  The 
latter  is  the  agency  by  which  the  electron  reorgan- 
izes its  wave  system  with  the  velocity  of  light, 
that  is  to  say,  by  which  the  field  of  the  electron 
receives  the  additional  magnetic  energy  necessary 
for  the  increase  of  the  kinetic  energy  associated 
with  an  increase  of  velocity,  or  restores  the  excess 
magnetic  energy  when  its  velocity  diminishes. 
It  is  through  the  acceleration  wave  that  the  magne- 
tic energy  of  change  corresponding  to  an  increase  or 
a  decrease  of  velocity  is  distributed  to  each  part 
of  the  wave  system  or  restored  in  the  form  of  work, 
this  magnetic  energy  being  in  the  first  case  bor- 
rowed from  external  actions  and  in  the  second  case 
restored  in  the  form  of  work  done  against  the 
retarding  actions.  The  energy  radiated  from  the 
acceleration  wave  represents  as  it  were  a  necessary 
shrinkage,  a  tribute  paid  to  the  auxiliary  wave  for 
the  service  rendered. 


ELECTRONIC    THEORY  115 

The  emission  of  radiation  is  always  connected  with 
acceleration  of  electrified  particles.  It  is  the  difference 
in  the  conditions  of  electrons  present  in  matter  that 
enables  us  to  explain  the  emission  of  different  kinds  of 
radiation  and  the  phenomena  traceable  to  them  such  as 
mutual  induction  and  self-induction. 

Let  us  consider  first  these  last  two  phenomena. 
Conduction  currents  are  reducible  to  convection 
currents:  they  correspond  to  the  mass  motion 
of  the  free  electrons  of  the  metallic  or  electrolytic 
conductors  under  the  influence  of  a  potential  dif- 
ference, the  positive  electrons  tending  to  go  in 
one  direction,  the  negative  in  the  other.  If  two 
wires  are  placed  side  by  side,  such  as  the  two  neigh- 
boring windings  of  a  transformer,  the  passage  of 
the  inducing  current  corresponds  to  the  circulation, 
in  the  first  wire,  of  free  electrons  of  which  it  is 
the  conductor.  The  intensity  of  the  current  is 
proportional  to  the  ensemble  velocity  of  these 
electrons,  and  any  variation  of  intensity  will  cor- 
respond to  an  acceleration  experienced  by  the  elec- 
trons. At  the  moment  when  the  current  varies, 
there  will  be  an  emission  of  acceleration  waves  by  the 
electrons  of  the  wire.  The  superposition  of  these 
waves  at  a  point  of  the  neighboring  wire  will  give 
rise  to. the  appearance  of  an  electric  field  parallel 
to  the  wire  and  in  the  opposite  direction  to  the 
current  if  the  intensity  increases,  in  the  same 
direction  if  it  diminishes.  In  the  case  when  this 
point  is  situated  inside  of  the  neighboring  wire, 
the  electric  field  thus  created  will  determine  a 


116  PHILOSOPHY    AND    THE    NEW    PHYSICS 

current,  corresponding  to  the  existence  of  an  elec- 
tromotive force,  the  direction  of  which  is  given  by 
Lenz's  law. 

The  phenomena  of  self-induction  are  explained 
in  the  same  manner.  If  the  intensity  of  the  current 
increases,  the  acceleration  waves  emitted  by  the 
electrons  when  their  velocity  varies  will  add  them- 
selves together  in  the  circuit  as  well  as  outside,  and 
produce  there  an  electric  field,  directed  oppositely 
to  the  current,  by  the  agency  of  which  the  energy 
necessary  for  the  growth  of  the  magnetic  field 
encircling  the  circuit  is  borrowed  from  the  electro- 
motive source  that  produces  the  current.  If  the 
current  diminishes,  the  accelerations  of  the  positive 
particles  being  opposed  to  the  direction  of  the  cur- 
rent, the  radiated  waves  produce  in  the  conductor 
an  electromotive  field  in  the  same  direction,  by  the 
agency  of  which  the  excess  of  energy  of  the  magnetic 
field,  which  encircles  it,  will  be  returned  to  the 
circuit. 

Conduction  currents  are  at  basis  only  con- 
vection currents;  the  explanation  of  their  '  self- 
induction  must  account  for  the  inertia  of  an  elec- 
trified particle  in  motion.  This  inertia  is  due  to  the 
production  of  a  magnetic  field  having  its  source 
in  the  displacement  of  the  particle,  and  to  the  fact 
that  the  energy  present  in  this  field  must  vary  with 
the  velocity  by  the  agency  of  the  acceleration 
wave.  The  force  of  inertia  that  the  particle 
opposes  to  the  change  of  velocity  comes  from 
the  action,  on  every  element  of  its  charge,  of  the 


ELECTRONIC    THEORY  117 

electric    field   present    in   the    acceleration   waves 
emitted   by   the     other   elements   of   this   charge. 

The  character  of  the  free  radiation,  which  mani- 
fests itself  in  the  form  of  Hertzian  waves,  of  light, 
of  Rontgen  rays,  and  of  thermal  radiations,  depends 
on  the  nature  of  the  electrons  that  are  accelerated 
and  on  the  circumstances  of  their  acceleration, 
sudden,  continuous,  or  periodic. 

A  sudden  acceleration  takes  place  on  the  arrest 
b^-  an  obstacle  of  the  cathode  particles  or  the 
]8  particles,  projected  with  velocities  comprised 
between  20.000  km.  and  290,000  km.  per  second. 
The  radiation  consists  in  a  sudden  pulsation,  a  kind 
of  electromagnetic  noise,  emitted  at  the  moment  of 
the  arrest  of  the  particle,  its  thickness  being  equal 
to  the  product  of  the  velocity  of  light  and  the  dura- 
tion of  the  shock,  that  is  to  say,  it  is  of  atomic 
dimensions.  This  extreme  thinness  explains  the 
penetrating  power  as  well  as  the  absence  of  refrac- 
tion of  X-rays. 

The  acceleration  is  periodic  in  the  case  of  the 
electrons  that  move  in  closed  curves  around  a  posi- 
tive center  inside  the  atoms.  From  it  there  results 
a  continual  emission  of  regular  waves,  the  period 
of  which  is  equal  to  the  time  of  revolution  of  the 
electrons.  This  emission  corresponds  to  light  of 
a  definite  wave-length,  like  that  which  constitutes 
discontinuous  spectra. 

If  the  acceleration  is  due  to  the  chaotic  agitation 
of  the  free  electrons  of  incandescent  sources,  there 
result  from  it  radiations  of  every  wave-length, 


118  PHILOSOPHY    AND    THE    NEW    PHYSICS 

which  form  the  continuous  spectra  of  incandescent 
bodies. 

If  the  radiation  is  due  to  the  accelerations  which 
the  free  electrons  of  an  opaque  metallic  enclosure 
undergo  as  a  consequence  of  the  thermal  agitation 
of  the  molecules  that  strike  them,  it  constitutes 
the  heat  radiation  inside  of  this  enclosure,  called 
black  radiation. 

The  presence  of  moving  electrons  in  matter  ex- 
plains not  merely  the  emission  of  radiation  but  also 
the  laws  of  its  propagation  through  material  media 
and  those  of  its  absorption. 

The  absorption  of  radiation  by  matter  is  due 
to  the  fact  that  the  electrons  present  in  the  matter 
are,  under  the  action  of  the  alternating  fields  of 
the  incident  electromagnetic  waves,  set  into  vibra- 
tion in  agreement  with  them.  In  consequence  of 
the  motions  thus"  produced,  they  strike  the  neigh- 
boring material  molecules,  the  kinetic  agitation  of 
which  they  increase  at  the  expense  of  their  vibra- 
tory energy.  It  is  by  this  mechanism  that  the 
electromagnetic  energy  of  the  absorbed  radiation 
is  changed,  through  the  agency  of  the  shocks,  into 
thermal  energy,  that  is,  into  kinetic  energy  of  cha- 
otic agitation  of  the  molecules  of  the  absorbing 
body.  It  is  because  of  this  that  a  body  which  ab- 
sorbs radiation  is  heated  at  the  expense  of  the  in- 
cident electromagnetic  energy,  and  that  its  mass 
is  increased  by  all  the  Maupertuisian  mass  of  the 
absorbed  radiation.  In  the  case  of  selective  ab- 
sorption it  is  not  the  free  electrons  but  the  elec- 


ELECTRONIC    THEORY  119 

trons  in  a  regular  periodic  motion  within  the 
atoms  which  absorb,  by  a  resonance  phenomenon, 
the  radiations  of  a  period  equal  to  that  of  their 
motions. 

In  conclusion,  the  electronic  theory  of  matter 
appears  to  give  an  account  of  the  mechanism  of  the 
relations  existing  between  matter  and  radiation. 
By  the  success  of  this  step,  the  electronic  theory 
is  correspondingly  strengthened.  It  reinforces 
the  view  that  at  basis  there  exists  only  electro- 
magnetic energy,  which  presents  itself  in  two  different 
aspects:  narrowly  circumscribed  and  concen- 
trated in  space  in  the  form  of  elementary  charges 
in  motion,  the  velocity  of  which  may  vary  from  0 
to  V;  and  in  the  form  of  radiation  sweeping  through 
all  space  with  the  rapidity  of  light — in  the  form  of 
grains  of  electricity  and  in  the  form  of  transverse 
waves  indefinitely  expansible  and  divisible — stabi- 
lized in  structures  of  varied  and  definite  architec- 
ture, or  free  to  lose  itself  by  radiation  to  infinity. 

The  success  of  the  electronic  theory  and  of  the 
mechanics  of  relativity  reduces  finally  the  prim- 
itive pluralism  of  ponderable  matter  and  imponder- 
able agents  to  the  dualism  of  negative  electricity 
(possibly  also  positive),  endowed  with  a  corpuscular 
structure  and  of  electromagnetic  radiation  formed  of 
continuous  waves,  both  of  them  having  inertia  and 
weight. 


120  PHILOSOPHY   AND   THE    NEW   PHYSICS 

18.    CHECK     TO     THE     ELECTRONIC     THEORY:     BLACK 
RADIATION     AND     THE     QUANTUM     THEORY. 

The  electronic  theory  has  nevertheless  reached  its 
limits:  it  has  been  revealed  as  incapable  of  giving 
an  account  of  the  law  of  the  distribution  of  energy 
in  the  spectrum  of  a  black  body  and  of  the  dimi- 
nution of  the  specific  heats  of  solids  at  low  tempera- 
tures, while  the  classical  theory  of  radiation,  due 
to  Maxwell  and  Hertz,  suffered  shipwreck  from 
certain  phenomena  of  physical  optics.  To  bring 
theory  and  experiment  into  accord  new  supple- 
mentary hypotheses  had  to  be  introduced.  Are  they 
going  to  modify  the  previously  acquired  results,  to 
give  support  to  a  dualism  between  matter  and  radi- 
ation? Far  from  it,  on  the  contrary  they  weaken 
it,  for  they  amount  to  nothing  less  than  endowing 
radiant  energy  with  structure,  after  it  has  already 
been  endowed  with  inertia  and  weight.  In  fact  they 
finally  lead  to  the  view  that  radiation  is  not  a 
system  of  waves  infinitely  expansible  and  divisible, 
propagated  by  a  hypothetical  medium,  the  ether, 
but  a  projection  of  matter  in  empty  space  with  the 
velocity  of  light,  in  discrete  units,  emitted  and  ab- 
sorbed by  bodies  in  a  discontinuous  manner.1 

In  order  to  understand  the  point  at  issue,  we  must 
begin  by  defining  what  black  radiation  is. 

Any  body  that  is  not  at  the  absolute  zero  emits 
energy  in  the  form  of  thermal  radiation.  When 

1  Cf.  La  thSorie  du  rayonnement  et  les  quanta  (Rapports  et  dis- 
cussions de  la  reunion  de  Bruxelles,  publics  par  P.  Langevin  et  M. 
de  Broglie,  Paris,  1912). 


BLACK    RADIATION  121 

unequally  hot  bodies  are  placed  in  an  enclosure 
observation  shows  that  they  finally  come  to  thermal 
equilibrium,  all  bodies  in  the  enclosure  reaching 
the  same  temperature.  This  equilibrium  can  have 
been  attained  only  by  exchange  of  radiation  between 
the  bodies.  When  it  is  attained  the  bodies  do  not 
radiate  less,  but  each  of  them  acquires  by  absorption 
as  much  as  it  expends  in  emission.  This  result  has 
led  KirchhofT  to  state  the  following  law  on  the  sub- 
ject of  thermal  radiation:  the  emissive  power  of 
a  body  for  every  kind  of  radiation  and  at  any  tem- 
perature is  equal  to  its  absorbing  power.  In  the 
case  of  an  ideal  black  body,  which  completely  ab- 
sorbs the  radiations  that  strike  it,  the  absorbing 
power  is  equal  to  unity.  We  are  thus  led  to  seek  for 
the  law  of  the  distribution  of  radiant  energy  in 
the  spectrum  emitted  by  a  black  body  at  a  given 
temperature. 

In  nature  there  exists  no  rigorously  black  body, 
no  body  that  does  not  reflect  or  diffuse  in  part  the 
radiation  that  it  receives.  Kirchhoff  has  enabled 
us^  to  get  over  the  difficulty  by  supplying  the 
means  of  realizing  a  black  body  artificially.  Let 
us  consider  an  opaque  enclosure  and  any  radiation 
whatever  that  is  propagated  inside  it:  it  will  strike 
the  wall  a  first  time  and  will  be  partly  absorbed; 
the  remaining  radiation,  reflected  or  diffused,  will 
again  strike  other  parts  of  the  wall  and  be  there 
absorbed  in  the  same  proportion,  so  that  the  radia- 
tion which  escapes  absorption  will  tend  rapidly 
towards  zero.  Such  an  enclosure  possesses  there- 


122  PHILOSOPHY    AND    THE    NEW    PHYSICS 

fore  an  absorbing  power  equal  to  unity  for  any 
radiation:  it  realizes  the  black  body. 

Let  us  plunge  this  enclosure,  after  having  evacu- 
ated it,  into  a  bath  at  constant  temperature,  so  as  to 
maintain  its  walls  at  constant  temperature.  Ex- 
periment proves  that  the  space  inside  this  enclosure 
is  isothermal,  that  is,  that  a  thermometer  placed  at 
any  point  whatever  inside  of  this  enclosure,  will 
finally  indicate  the  same  temperature.  Any  action 
on  the  thermometer  placed  in  'the  vacuum  must 
be  exerted  by  radiation.  In  the  region  where  the 
thermometer  is  placed,  undulations  arriving  inces- 
santly from  different  points  of  the  enclosure  become 
superimposed  and  form  systems  of  stationary  waves 
of  definite  frequency,  adapted  to  the  distances  ex- 
isting between  two  walls  and  realizing  a  permanent 
state  of  extremely  rapid  changes,  the  details  of 
which  are  beyond  our  scale  of  time  measurement. 
This  is  what  is  expressed  by  saying  that  the  thermal 
equilibrium  realized  in  the  interior  of  the  enclosure 
is  a  statistical  equilibrium.  This  equilibrium  is  real- 
ized for  every  kind  of  radiation  separately,  and.  it 
is  characterized  by  the  amount  of  energy  that  is 
contained  per  unit  volume  in  the  space  within  the 
enclosure  and  by  the  distribution  of  this  energy 
between  the  different  wave  lengths  of  the  systems 
of  stationary  waves.  It  is  precisely  this  energy 
density  and  this  distribution  of  energy  in  the  spec- 
trum that  has  to  be  determined  for  black  radiation. 

This  we  succeed  in  doing  by  the  following  method. 
Experiment  proves  that  the  temperature  indicated 


BLACK    RADIATION  123 

by  the  thermometer  is  independent  of  the  nature, 
the  shape  and  the  dimensions  of  the  walls  of  the 
enclosure.  It  follows  therefrom  that  all  the  direc- 
tions are  equivalent  and  that  each  cubic  centimeter 
of  the  enclosure  contains  the  same  density  of 
radiant  energy.  If  we  consider  in  the  enclosure 
a  plane  closed  contour  of  one  square  centimeter 
surface,  the  amount  of  radiation  that  passes  through 
this  contour  in  one  second  will  have  a  definite  value, 
proportional  to  the  density  of  the  energy  of  radi- 
ation in  equilibrium  at  this  temperature.  To  study 
the  composition  of  the  radiation  of  the  isothermal 
enclosure,  which  is  identical  with  that  of  a  black 
body  and  on  that  account  is  called  black  radiation, 
it  will  be  sufficient  to  make  a  small  opening  in  the 
enclosure,  so  as  to  collect  the  radiation  that  comes 
out  of  it  and  that  we  know  to  be  identical  with  the 
radiation  which  in  the  isothermal  enclosure  traver- 
ses at  every  instant  a  section  of  equal  contour. 
By  this  device  we  can  deduce  Stefan's  law  for  the 
density  of  radiated  energy:  the  density  of  the 
total  energy  radiated  per  unit  time  is  proportional 
to  the  fourth  power  of  the  absolute  temperature. 
By  receiving  the  radiation  in  a  dispersing  apparatus 
it  has  been  found,  as  regards  the  distribution  of 
energy  in  the  spectrum,  that  at  a  given  temperature 
the  energy  radiated  shows  a  maximum  for  a  certain 
definite  radiation  on  both  sides  of  which  it  decreases 
rapidly.  When  the  temperature  rises  the  energy 
density  of  each  simple  radiation  always  increases, 
but  the  maximum  of  intensity  is  displaced  towards 


124  PHILOSOPHY    AND    THE    NEW    PHYSICS 

the  shorter  wave-lengths,  that  is,  for  the  visible 
part  of  the  emitted  spectrum,  from  the  infra-red 
towards  the  ultra-violet.  The  curve  of  intensities 
becomes  displaced  along  the  spectrum,  mounting 
more  and  more,  at  first  slowly,  then  with  an  extreme 
rapidity  the  higher  the  temperature  rises.  Wien 
has  discovered  the  law  of  this  displacement  as  a 
function  of  the  wave  length  for  a  given  temperature, 
and  this  determines  the  distribution  curve  of  the 
total  energy  of  the  spectrum  of  a  black  body:  the 
wave  length  corresponding  to  the  intensity  maxi- 
mum decreases  inversely  as  the  absolute  temper- 
ature, while  the  intensity  of  the  maximum  increases 
in  proportion  to  the  fifth  power  of  the  absolute 
temperature. 

It  remained  to  express  in  a  single  empirical 
formula  the  distribution  in  the  spectrum  of  the 
intensities  of  the.  black  radiation  for  all  the  tem- 
peratures observed:  this  is  what  Max  Planck  has 
succeeded  in  doing,  and  it  is  the  physical  interpreta- 
tion of  this  formula  that  is  the  starting  point  of 
the  quantum  theory. 

In  the  isothermal  enclosure  thermal  equilibrium 
exists  between  the  matter  of  the  walls  and  the 
empty  space  (or  ether)  in  which  there  is  black  radi- 
ation. The  temperature  of  the  walls  is  due  to  the 
internal  agitation  of  the  molecules  that  constitute 
them;  the  temperature  of  the  empty  space  is  due  to 
the  stationary  waves  that  exist  between  the  walls. 
This  thermal  equilibrium  between  matter  and 
radiation  is  realized  by  the  mechanism  previously 


BLACK   RADIATION  125 

described.  The  molecules  of  the  walls  of  the 
enclosure  in  their  kinetic  agitation  hit  the  free 
electrons  existing  in  the  walls.  As  a  consequence 
of  these  shocks  the  electrons  undergo  accelerations 
that  determine  a  radiation  of  all  wave  lengths, 
the  electromagnetic  energy  of  which  is  borrowed 
from  the  thermal  energy  of  the  molecular  agita- 
tion: the  temperature  of  the  empty  space  is  increa- 
sed at  the  expense  of  that  of  the  matter. 

Reciprocally,  and  by  a  mechanism  inversely 
symmetrical,  the  electrons,  being  subjected  to  the 
action  of  the  radiations,  vibrate  in  resonance  with 
them.  In  consequence  of  the  oscillations  thus  star- 
ted they  strike  the  neighboring  molecules,  the  ther- 
mal agitation  of  which  increases :  the  temperature  of 
the  matter  is  increased  at  the  expense  of  that  of  the 
empty  space.  There  is  thermal  equilibrium  be- 
tween the  matter  and  the  radiation,  when  there  is 
equality  between  the  exchanges  of  energy  brought 
about  by  means  of  the  electrons. 

The  aggregate  of  the  material  molecules,  the 
electrons,  and  the  various  stationary  waves  that 
exist  in  the  empty  space,  form  a  system  in  statistical 
equilibrium  to  which  can  be  applied  the  laws  of 
statistical  mechanics,  in  particular  the  theorem, 
discovered  by  Maxwell,  correctly  demonstrated  by 
Boltzmann,  which  siims  up  the  properties  of  such 
systems.  This  is  the  law  of  the  equipartition  of 
energy.  It  states  that  in  a  thermal  system  the 
mean  kinetic  energy  is  divided  equally  among  all 
the  degrees  of  freedom  of  the  system. 


126  PHILOSOPHY    AND    THE    NEW    PHYSICS 

By  degrees  of  freedom  of  a  system  are  meant  the 
different  motions  that  it  can  assume  consistently 
with  the  connections  to  which  it  is  subject.  For 
example,  a  material  point  can  move  along  three 
axes,  it  has  three  degrees  of  freedom;  a  sphere  can 
undergo  a  translation  parallel  to  each  of  these  three 
axes  and  a  rotation  about  these  axes,  it  has  six  de- 
grees of  freedom.  The  molecule  of  a  monatomic 
gas,  like  argon,  is  supposed  to  have  three  degrees  of 
freedom;  a  molecule  of  oxygen  five;  a  triatomic  mole- 
cule six,  three  degrees  of  translation  and  three  de- 
grees of  rotation.  If  the  law  of  equipartition  is 
applied  to  a  gas  in  thermal  equilibrium,  the  vis  viva 
which,  on  the  average,  each  molecule"  will  have,  is 
proportional  to  the  number  of  its  degrees  of  freedom : 
if,  in  the  statistical  equilibrium,  a  molecule  of  argon 
possesses  at  a  certain  temperature  the  vis  viva  3,  a 
molecule  of  oxygen  must  possess  the  vis  viva  5. 

This  law,  which  results  from  the  Hamiltonian  form 
of  the  equations  of  dynamics,  must  be  applicable 
to  the  statistical  system  constituted  by  the  material 
walls  of  the  enclosure  and  the  black  radiation.  It 
will  be  sufficient  to  count  the  number  of  the  degrees 
of  freedom  of  the  system  to  predict,  by  this  law,  the 
most  probable  spectral  composition  of  radiation  in 
the  state  of  thermal  equilibrium,  the  realization  of 
which  is  a  necessary  physical  consequence  of  Carnot's 
principle.  We  have  to  consider  on  one  hand  the 
molecules  of  the  material  walls,  on  the  other  hand 
the  various  systems  of  stationary  waves  possible  in 
the  empty  space.  Let  N  be  the  number  of  the 


BLACK    RADIATION  127 

material  molecules  contained  in  the  walls  of  the 
enclosure;  the  number  of  their  degrees  of  freedom 
being  equal  to  6,  there  will  be,  for  the  matter,  as  a 
consequence  of  its  discontinuity,  only  a  finite  num- 
ber of  degrees  of  freedom,  namely  67V.  Let  us  con- 
sider on  the  other  hand  the  empty  space.  It  has  an 
infinite  number  of  degrees  of  freedom,  for  there  is  an 
infinite  number  of  systems  of  possible  stationary 
waves,  the  wave-lengths  of  which  lie  between  oo  and 
0.  Hence,  if  the  law  of  equipartition  among  all  the 
degrees  of  freedom  is  applied,  the  energy  will  be 
found  entirely  in  .the  empty  space  and  none  would 
remain  for  the  matter :  equilibrium  would  cease  to  be 
possible,  or  rather  a  single  state  of  equilibrium  only 
would  be  possible,  that  in  which  the  matter  is  at  the 
absolute  zero.  Moreover,  the  energy  received  by 
the  space  must  be  equally  apportioned  among  its 
degrees  of  freedom,  infinite  in  number.  Whatever 
might  be  the  amount  of  the  total  energy,  that  assign- 
ed to  each  degree  of  freedom  would  be  zero,  at  least 
if  the  quantity  of  energy  at  our  disposal  is  not  in- 
finite, which  has  no  physical  meaning.  This  would 
be  no  longer  the  case  if  it  were  assumed  that  the 
length  of  the  luminous  oscillations  can  not  descend 
below  a  certain  limit  X0.  This  would  bring  us  back 
to  assuming  an  ether  and  endowing  it  with  structure. 
In  fact,  what  limits  the  periodic  motions  that  can  be 
propagated  in  a  given  medium  is  the  necessity  that 
their  wave-lengths  be  appreciably  larger  than  the 
scale  of  the  structure  of  the  medium.  The  wave- 
length of  sounds  given  by  a  vibrating  cord  must  be 


128  PHILOSOPHY    AND    THE    NEW   PHYSICS 

greater  than  the  mutual  distance  of  the  molecules 
that  constitute  the  cord  or  the  sounds  would  not 
exist.  In  the  same  way  the  seismic  waves  that 
traverse  a  continent  have  reality  only  for  an  observer 
whose  horizon  extends  beyond  the  region  of  local 
variations.  Similarly,  if  a  structure  of  the  ether  ex- 
ists, we  can  no  longer  speak  of  infinitely  small 
wave-lengths  in  the  mathematical  sense  of  the  word : 
the  smallest  wave-lengths  that  it  would  be  possible 
to  assume  are  those  for  which  the  magnitude  X  is 
near  the  number  that  measures  the  distance  between 
two  ether  molecules.  The  number  of  degrees  of  free- 
dom of  the  ether  would  be  limited  in  number,  and 
thermal  equilibrium  between  matter  and  ether  then 
becomes  possible. 

This  idea  has  the  disadvantage  of  being  based 
on  the  hypothetical  existence  of  the  ether,  and  of  an 
ether  endowed  with  discontinuous  structure,  which 
is  not  readily  conceived.  But,  moreover,  it  is 
ineffective,  for  it  leads  to  predictions  at  variance 
with  experiment.  In  fact,  the  number  of  systems 
of  stationary  waves  the  wave-length  of  which  lies 
between  the  limits  X  and  X  +  d\  is  greater  the 
smaller  X  is.  The  result  would  be  that  the  degrees 
of  freedom  of  the  smallest  wave-lengths  would  tend 
to  appropriate  all  the  disposable  energy,  which 
would  be  dissipated  in  extremely  short  radiations, 
and  this  is  contrary  to  experiment.  Thus  the 
preceding  hypothesis  leads  to  a  wrong  law,  formu- 
lated first  by  Lord  Rayleigh  and  Jeans  as  a  conse- 
quence of  the  equipartition  of  energy,  that  the 


QUANTUM    THEORY  129 

energy  radiated  for  a  given  wave-length  is  propor- 
tional to  the  absolute  temperature  and  varies 
inversely  as  the  fourth  power  of  the  wave-length. 

To  escape  from  these  difficulties,  Planck  has 
put  forth  a  radical  hypothesis,  which  has  the  merit 
of  being  free  from  the  consideration  of  any  hypothe- 
tical medium  and  considers  nothing  but  the  only 
positively  accessible  reality,  energy.  The  formula 
that  he  has  proposed  for  representing  the  distribu- 
tion of  energy  in  a  black  spectrum  amounts  to  sub- 
stituting discontinuous  series  of  elements,  the  sum 
of  which  remains  always  finite,  for  an  integral  which 
occurs  in  the  mathematical  expression  of  Lord 
Rayleigh's  law  and  which  has  the  disadvantage  of 
becoming  infinite.  He  interprets  this  discontinuity, 
not  by  hypotheses  on  the  structure  of  the  medium 
in  which  the  radiant  energy  moves,  but  by  hypo- 
theses on  the  absorption  and  emission  of  this  energy  v 
According  to  him  the  exchanges  of  energy  between 
radiation  and  matter  cannot  take  place  in  a  con- 
tinuous manner  in  any  proportion  whatever,  for 
this  introduces  an  infinite  number  of  degrees  of 
freedom,  but  they  must  take  place  in  a  discontinu- 
ous manner  in  definite  proportions.  The  electric 
resonators  (free  electrons)  through  the  agency  of 
which  these  exchanges  are  realized  can  only  absorb 
or  emit  radiant  energy  in  a  discontinuous  manner, 
by  sudden  jumps,  according  to  integral  multiples 
of  elementary  quantities,  indivisible  energy  atoms 
called  quanta.  These  quanta,  which  fix  the  lower 
limit  of  intake  and  output  of  energy,  are  not  the 


130  PHILOSOPHY    AND    THE    NEW   PHYSICS 

same  for  all  the  resonators:  they  are  inversely 
as  the  wave-length  (or  the  period  of  their  oscillation) 
and  connected  with  the  frequency  v  according  to 
the  relation 

(21)  q  =  hv 

where  h  represents  a  universal  constant.  As  a  con- 
sequence of  this  hypothesis  the  resonators  of  short 
period  can  absorb  and  emit  energy  only  in  large 
mouthfuls,  while  the  resonators  of  long  period  can 
swallow  and  give  it  up  in  small  morsels.  It  re- 
quires a  large  amount  of  disposable  energy  to  rouse 
a  resonator  of  short  period,  so  that  the  resonators 
of  this  kind  will  have  a  chance  to  remain  at  rest, 
especially  if  the  temperature  is  low.  By  this  means 
the  noxious  role  of  the  wave-lengths  near  zero,  the 
presence  of  which  made  the  equilibrium  impossible, 
is  eliminated.  Thereby  also  the  fact  is  explained 
that  there  is  relatively  little  light  of  short  wave- 
length in  black  radiation,  which  is  in  accord  with 
Planck's  empirical  formula.  On  the  other  hand, 
the  discontinuity  in  the  intake  and  output  of  the 
energy,  which  is  progressively  accentuated  and  be- 
comes enormous  for  short  wave-lengths,  tends  to 
disappear  in  the  region  of  large  wave-lengths,  where, 
as  the  result,  Lord  Rayleigh's  law  is  found  again  to 
hold. 

Let  us  consider  our  isothermal  enclosure  and  see 
what  happens  when  the  temperature  is  progres- 
sively raised,  starting  from  the  absolute  zero.  At 
first  the  molecules  are  motionless  and,  as  it  were, 


QUANTUM    THEORY  131 

anchylosed  by  the  frost,  the  thermal  energy  is  zero, 
the  resonators  are  mute.  If  the  temperature  is 
raised,  the  resonators  whose  quantum  is  the  smallest 
will,  because  of  the  incipient  molecular  agitation, 
begin  to  vibrate,  and  the  first  radiations  will  appear 
in  the  infra-red  which  is^far  removed  from  the  visi- 
ble spectrum.  Step  by  step  the  other  resonators 
will  begin  to  be  agitated  and  the  spectrum  will  be 
extended  towards  the  luminous  radiations,  then 
towards  the  ultra-violet,  in  conformity  with 
Planck's  law  and  with  what  experiments  reveal  to 
us.  The  quantum  increasing  indefinitely  as  X  tends 
towards  0,  the  radiations  corresponding  to  the  limit 
will  never  appear. 

Planck's  theory  seems  thus  to  imply  that  the 
Structure  of  energy  is  discontinuous.;  Every  reso- 
nator can  emit  or  absorb  only  a  whole  number  of 
grains  of  energy.  The  value  of  this  grain  depends 
uniquely  on  the  frequency  v  of  this  resonator  and 
is  proportional  to  it.  There  are  atoms  of  energy, 
as  there  are  atoms  of  electricity  and  atoms  of  matter 
formed  of  the  first.  However,  while  a  hydrogen 
atom  conserves  its  mass,  whatever  be  the  compound 
into  which  it  enters,  while  the  atom  of  electricity 
conserves  its  individuality  through  any  vicissitude 
that  it  undergoes,  it  is  not  the  same  with  the  quanta 
of  energy.  If  we  have,  for  example,  three  quanta 
of  energy  on  a  resonator  the  wave-length  of  which 
is  3,  and  if  this  energy  passes  to  a  second  reso- 
nator the  wave-length  of  which  is  5,  it  represents 


132  PHILOSOPHY   AND    THE    NEW    PHYSICS 

no  longer  3  but  5  quanta  of  energy.  This  is  one 
of  the  numerous  difficulties  of  the  theory. 

One  of  the  confirmations  of  the  quantum  theory 
is  drawn  from  the  determination  of  Avogadro's 
constant  (the  number  of  molecules  contained  in  a 
gram-molecule  of  a  gas)  which  it  provides.  Two 
constants  figure  in  Planck's  empirical  formula:  one 
which  expresses  the  discontinuity  of  the  energy  of 
oscillation  of  resonators,  called  the  universal  constant 
h,  another  which  expresses  the  molecular  disconti- 
nuity, called  Avogadro's  constant  N.  To  determine 
the  numbers  h  and  TV  it  suffices  to  use  two  good 
measurements  of  the  emissive  power  (the  quantity 
of  energy  that  leaves  the  opening  of  the  enclosure 
per  second)  for  different  values  of  the  wave  length 
X  and  the  temperature  T.  The  value  of  h  is  then 
found  to  be 

h  =  6.2  X  10-27 

and  this  leads  to  the  value  of  N 
N  =  64  X  1022 

This  number  agrees  quite  closely  with  the  mean  of 
the  numbers  obtained  by  the  methods  considered 
most  reliable,  and  this  coincidence  is  the  more  sur- 
prising as  the  number  of  molecules  is  deduced  from 
measurements  made  on  radiant  heat. 

A  second  confirmation,  due  to  Einstein  and  to 
Nernst,  is  drawn  from  the  study  of  the  specific  heats 
of  solids  at  low  temperature.  It  is  known  that 
the  specific  heats  of  solids  decrease  rapidly  when 
the  temperature  is  lowered.  Thus,  for  diamond 


QUANTUM    THEORY  133 

at  the  temperature  of  liquid  hydrogen,  the  specific 
heat  is  reduced  to  about  one-seventh  of  what  it  is 
at  ordinary  temperatures.  Everything  takes  place 
as  if  the  molecules  lost  degrees  of  freedom  in  cool- 
ing, as  if  their  joints  became  anchylosed  from  the 
effect  of  the  frost.  This  is  contrary  to  the  the- 
orem of  the  equipartition  of  energy,  which  provides 
a  method  of  calculating  the  atomic  heats  of  solids 
and  of  deducing  Dulong  and  Petit's  law,  accord- 
ing to  which  the  atomic  heats  are  equal  for  all  bodies 
and  independent  of  the  temperature. 

Planck  defined  the  specific  heat  of  a  single 
resonator  as  the  increase,  for  one  degree  centigrade, 
of  the  mean  energy,  reduced  to  calories,  that  a 
resonator  of  given  frequency  must  have  at  a  definite 
temperature  to  be  in  equilibrium  with  black  radi- 
ation. Einstein  introduces  the  following  simpli- 
fying hypotheses.  He  considers  the  solid  bodies  as 
possessing  only  a  single  kind  of  resonators  and  only 
one  resonator  per  molecule;  the  product  of  Avoga- 
dro's  constant  by  the  specific  heat  of  a  single 
resonator  then  gives  him  the  specific  heat,  referred 
to  a  gram-molecule,  of  the  solid  considered.  Accord- 
ing to  this  formula  the  specific  heat  of  a  solid 
hardly  varies  with  the  change  of  temperature 
at  high  temperatures;  but  at  low  temperatures  it 
decreases  rapidly  and  tends  towards  zero  when  the 
absolute  zero  is  approached.  Nernst  complicates 
Einstein's  hypothesis  a  little  by  adding  to  the  lat- 
ter's  unique  system  of  resonators  other  resonators 
tuned  to  the  octave  and  so  succeeds  in  obtaining 


134  PHILOSOPHY   AND    THE    NEW    PHYSICS 

a  surprising  coincidence  with  the  numbers  obtained 
experimental!}'  by  himself  and  his  pupils,  for  a  very 
large  number  of  bodies  at  temperatures  that  extend 
from  the  ordinary  temperatures  down  to  the  low- 
est temperatures  that  Kammerlingh-Onnes  has  been 
able  to  obtain  in  his  cryogenic  laboratory  at  Ley  den. 
This  theory  amounts  to  the  following:  if  a  solid 
is  regarded  as  an  aggregate  of  atoms  or  of  molecules 
oscillating  about  an  equilibrium  position,  the  en- 
ergy of  each  oscillator  thus  realized  must  be,  as  in 
the  case  of  Planck's  electric  oscillators,  an  inte- 
gral multiple  of  hv.  The  diminution  of  the  speci- 
fic heat  of  the  solid  at  low  temperatures  is  then 
readily  explained.  When  the  temperature  de- 
creases, the  supply  of  disposable  energy  offered 
to  each  of  the  material  oscillators  falls  below  the 
quantum  of  a  large  number  of  them;  instead  of 
vibrating  a  little  they  cease  to  vibrate  at  all,  so  that 
the  total  energy  diminishes  more  rapidly  than  in 
the  old  theories.  On  the  contrary,  at  high  tem- 
peratures, the  quantum  hv  becomes  so  small  that  we 
again  get  Dulong  and  Petit'slaw,  obtained  by  start- 
ing from  the  law  of  the  equipartition  of  energy. 

19.    THE  STRUCTURE  OF  RADIATION. 

The  study  of  black  radiation  and  of  specific 
heats  at  low  temperatures  has  led  Planck,  and  after 
him,  Einstein  to  the  idea  that  the  exchanges  between 
radiation  and  matter  do  not  take  place  in  a  continu- 
ous manner,  but  by  discrete  elements,  by  quanta  of 
energy.  What  becomes  of  these  elements  when  once 


STRUCTURE    OF   RADIATION  135 

set  free  by  matter?  For  the  old  theory  of  free 
radiation  considered  as  formed  by  indefinitely  di- 
visible and  expansible  spherical  waves  propagated 
by  a  continuous  hypothetical  medium,  there  is  now 
substituted  the  idea  of  a  radiation  projected  in 
space  void  of  matter  in  the  form  of  distinct  ele- 
mentary units,  which  implies  a  discontinuous  dis- 
tribution of  energy  in  the  front  of  the  luminous 
transverse  waves.  This  is  an  unexpected  return 
to  the  emission  theory,  rendering  the  consideration 
of  an  ether  serving  as  the  "I"  to  the  verb  "undulate" 
superfluous. 

Among  the  phenomena,  the  interpretation  of 
which  suggests  this  point  of  view,  we  have  Hertz's 
phenomenon  and  the  production  of  rays  by  shocks 
of  secondary  cathode  rays  and  by  X-rays. 

Hertz's  phenomenon,  or  the  photo-electric  effect, 
denotes  the  property  that  bodies  have,  in  particular 
metals,  of  emitting  cathode  rays  under  the  action  of 
light.  The  electric  forces  present  in  the  absorbed 
luminous  waves  set  the  electrons  stored  in  the  metal 
in  motion,  and  some  of  them  are,  because  of  the 
accelerations  that  they  undergo,  projected  out. 
The  photo-electric  current,  which  results  there- 
from, depends  on  two  factors,  the  number  of  the 
electrons  emitted  per  unit  time  and  the  velocity 
with  which  these  electrons  are  emitted.  If  the 
intensity  of  the  light  is  increased  without  a  change 
in  its  wave-length,  the  number  of  the  electrons 
emitted  increases  proportionally,  but  the  velocity 
of  emission  remains  the  same.  If,  on  the  other 


136  PHILOSOPHY   AND   THE   NEW    PHYSICS 

hand,  at  constant  luminous  intensity  a  change 
is  made  in  the  frequency  v  of  the  exciting  light, 
the  velocity  of  emission  seems  to  increase  propor- 
tionally to  the  frequency,  and  consequently  in- 
versely as  the  wave  length.  The  velocity  with 
which  the  electrons  are  emitted  certainly  did  not 
belong  to  them  before  they  had  undergone  the  action 
of  the  light,  as  experiment  shows  that  this  velocity 
is  very  much  higher  than  that  of  the  thermal  agita- 
tion. If  the  velocity  of  the  electrons  is  borrowed 
from  the  light,  how  are  we  then  to  understand  that 
it  is  the  same  for  a  very  intense  light  and  a  very  fee- 
ble light?  How,  above  all,  explain  that  it  varies 
inversely  as  the  wave  length? 

Stark1  has  remarked  that  these  difficulties  dis- 
appear if  the  quantum  hypothesis  is  assumed. 
The  light  that  meets  the  metal  is  not  of  homo- 
geneous structure,  it  consists  of  isolated  elements 
each  possessing  the  energy  hv.  When  one  of  these 
elements  strikes  the  metal  the  energy  that  it  con- 
tains can  pass  to  one  of  the  electrons  present  in  the 
metal.  On  account  of  this  fact  the  electron  acquires 
a  velocity  that  can  much  surpass  the  velocity  of 
thermal  agitation  and  leads  to  its  projection  from 
the  metal.  As  the  elements  of  energy  are  greater  in 
proportion  as  the  frequency  v  is  higher,  ultra-violet 
light  will  be  much  more  effective  than  visible  light. 
Thus  not  only  is  light  absorbed  and  emitted  solely  in 
the  form  of  quanta,  but,  even  when  it  is  freely  pro- 

1  Stark,  Phys.  Zeitschr.,  1909;  Principien  der  Atomdynamik. 
Leipzig,  1910. 


STRUCTURE    OF   RADIATION  137 

pagated  in  empty  space,  it  seems  to  consist  of  the 
projection  of  discrete  units. 

J.  J.  Thomson1  has  arrived  at  similar  conclu- 
sions by  studying  the  photo-electric  effect  on  gase- 
ous bodies.  Ultra-violet  light  of  very  short  wave- 
length ionizes  gases,  that  is,  it  breaks  up  the  gaseous 
molecules  by  setting  electrons  free.  The  work 
necessary  for  this  rupture  can  be  determined.  It 
is  thus  found  that  if,  in  conformity  with  Maxwell's 
ideas,  ultra-violet  light  is  thought  of  as  formed 
by  a  train  of  homogeneous  waves  propagated  with- 
out inequalities  of  structure,  the  energy  carried 
through  a  unit  section  is  not  sufficient  to  account  for 
the  work  of  ionization  produced  by  this  pencil.  To 
do  this  a  discontinuous  front  must  be  assumed,  so 
that  there  are  spots  of  light  and  darkness.  At 
places  where  the  energy  is  accumulated  its  density 
is  sufficient  to  ionize  the  molecules.  The  wave 
front  possesses  a  structure,  and  the  wave  train,  taken 
as  a  whole,  is  not  formed  of  a  regular  and  uninter- 
rupted flow  of  energy,  but  of  discrete  elements  of 
energy  separated  by  considerable  gaps.  This  is 
the  old  emission  theory  reappearing  in  a  very  modi- 
fied form. 

Einstein  has  supplemented  Stark's  ideas  in  a  way 
that  has  made  a  new  experimental  verification  of 
the  quantum  theory  possible.  He  assumes  that  an 
electron  set  free  by  a  luminous  ray  of  frequency 
v  can  bring  into  action  only  an  amount  of  energy 
equal  to  Planck's  energy  element.  Consequently 

1  J.  J.  Thomson,  Proceed.  Camb.  Phil.  Soc.,  1908. 


138  PHILOSOPHY   AND    THE    NEW   PHYSICS 

we  have,  according  to  the  principle  of  the  conserva- 
tion of  energy,  the  equality 

%mv2  =  hv  —  V 

where  ^  denotes  the  work  necessary  to  separate 
the  electron  from  the  atom  from  which  it  comes. 
This  formula  is  capable  of  direct  verification,  if  we 
take  into  account  the  fact  that  the  velocity  v  of  the 
photo-electric  electrons  can  be  determined  ex- 
perimentally by  the  measurement  of  the  condenser 
potential,  V  +  Fo,  capable  of  reducing  the  current 
to  zero,  by  reducing  the  velocity  v  to  zero.  We 
have 

e(V  +  Fo)  =  Mm*;2 

where  V  denotes  the  potential  difference  applied, 
and  V0  the  contact  potential  difference  that  always 
exists  between  two  different  metals,  and  these  two 
differences  have  to  be  determined  separately. 
Among  the  most  satisfactory  verifications  of  this 
formula,  the  recent  experiments  of  Millikan1  must 
be  quoted.  Working  in  a  vacuum  on  freshly 
prepared  surfaces  of  sodium,  potassium,  and  lith- 
ium, this  physicist  has  employed  the  entire  range 
of  wave-lengths  from  the  middle  of  the  visible 
spectrum  to  the  ultra-violet  of  the  mercury  arc. 
His  results  confirm  Einstein's  theory.  In  parti- 
cular, the  linear  relations  that  he  obtains  between 
V  and  v  make  possible  the  determination  of  a  con- 
stant angular  coefficient  practically  equal  to  Planck's 
constant. 

1 R.   A.    Millikan,   A   Direct   Photoelectric   Determination   of 
Phanck's  "h."    Phys.  Rev.  Ser.  2,  vol.  7,  p.  355. 


STRUCTURE    OF   RADIATION  139 

Lorentz1  has  shown,  not  only  that  the  corpuscular 
idea  of  light  results  from  Hertz's  phenomenon,  but 
that  it  alone  permits  the  explanation  of  the  absorp- 
tion of  radiation  by  fixed  quanta,  multiples  of  hv, 
in  conformity  with  the  views  of  Planck.  When 
an  incident  wave,  encountering  the  molecules  of  an 
isotropic  body,  sets  the  electrons  in  it  into  vibration, 
the  absorption  of  light  is  the  more  intense  the  nearer 
its  frequency  is  to  the  natural  frequency  of  these 
electrons.  In  the  case  of  perfect  resonance  the 
electron  borrows  from  the  luminous  wave  the  maxi- 
mum amount  of  energy,  and,  by  taking  the  case  of 
the  solar  light  and  allowing  for  the  forces  of  damp- 
ing and  friction  to  which  the  electron  is  subject, 
this  maximum  energy  is  found  by  calculation  to  be 
a  little  more  than  twice  the  atom  of  energy  required 
by  Planck.  A  similar  amount  of  light,  therefore, 
can  be  absorbed  by  the  electrons.  But  the  ordinary 
sources  have  intensities  a  million  times  weaker 
than  that  of  the  Sun.  If  the  energy  that  they  emit 
were  uniformly  distributed  over  the  surface  of  a 
sphere  having  the  source  as  center,  it  could  com- 
municate to  the  electron  only  a  very  small  fraction 
of  its  absorbable  quantum.  This  energy,  therefore, 
must  be  unequally  concentrated  in  different  direc- 
tions, and  the  sphere  must  be  traversed  by  the  flow 
of  energy  in  a  certain  number  of  discontinuous 
spots,  very  widely  spaced,  to  provide  condensations 
of  energy  compatible  with  the  mechanism  of  absorp- 
tion conceived  by  Planck. 

1  H.  A.  Lorentz,  Phys.  Zeitschr.,  1910. 


140  PHILOSOPHY   AND    THE    NEW    PHYSICS 


The  quantum  theory,  it  is  hardly  necessary 
to  say,  encounters  otherwise  many  difficulties. 
One  is  the  existence  of  interferences  at  large  differ- 
ences of  path,  which  seems  to  imply  that  the  lum- 
inous quanta  extend  over  lengths  equal  to  several 
thousand  times  their  wave-length.  There  are 
others  which,  however,  yield  to  a  deeper  analysis. 
The  idea  that  a  point  source  does  not  radiate 
symmetrically  in  all  directions  may  seem  incom- 
patible with  experiment.  But  the  physical  point 
sources  contain  a  number  of  oscillators  sufficiently 
great  to  wipe  out  any  trace  of  individual  discontin- 
uity. The  physical  symmetry,  which  experiment 
leads  us  to  attribute  to  luminous  waves,  results 
from  a  mean  effect  and  is  not  in  contradiction  to 
the  possibility  of  an  elementary  radiation,  endowed 
with  structure.  This  has  been  shown  by  J.  J. 
Thomson1  by  supposing  that  the  electrified  parti- 
cles producing  the  light  do  not  emit  lines  of  force 
uniformly  in  all  directions,  but  only,  for  example, 
in  two  solid  angles  opposed  at  the  vertex  and  of 
relatively  restricted  aperture.  Starting  from  this 
hypothesis,  he  has  demonstrated  that  the  principal 
properties  of  the  electron  would  still  belong  to  those 
particles,  the  electromagnetic  field  of  which  is 
concentrated  in  privileged  directions.  They  would 
have  inertia  of  electromagnetic  origin  and  would 
emit  radiation  on  every  modification  of  their  state 
of  motion;  but  the  radiated  waves  of  acceleration, 
light,  if  we  are  concerned  with  periodic  waves, 

1  J.  J.  Thomson,  Phil.  Mag.,  1910,  p.  301. 


STRUCTURE    OF   RADIATION  141 

would  be  concentrated  in  certain  directions  and 
extraordinarily  rarified  or  absent  in  others.  The 
radiation  emitted  by  an  oscillator  would  possess 
a  particular  structure,  which  would  reappear  in 
part  in  the  emission  of  real  sources  and  produce  the 
irregularities  of  the  wave  front  suggested  by 
Hertz's  phenomenon.  Nothing  essential  would  be 
changed  in  the  usual  laws  of  electromagnetism, 
and  they  would  continue  applicable  to  material 
complexes  enclosing  a  large  number  of  particles 
distributed  according  to  the  law  of  chance.  • 
V'The  quantum  theory  is  far  from  having  the 
dogmatic  certainty  of  the  atomic  theory  or  the 
electronic  theory.  The  atoms,  for  example,  have 
become  a  physical  reality:  they  are  counted, they 
are  weighed,  their  radius  of  action  and  their  mean 
velocity  are  determined,  they  are  seen  in  the  form 
of  scintillations  with  the  aid  of  the  spinthariscope 
of  Crookes,  and  C.  T.  R.  Wilson,  by  using  their 
property  of  becoming  the  centers  of  condensation  in 
supersaturated  water  vapor,  has  succeeded  in 
photographing  the  atomic  trajectory  of  the  a 
particles,  which  are  ions  of  helium,  and  even  the 
corpuscular  trajectory  of  the  0  rays,  which  are 
electrons.  No  device,  up  to  the  present,  has 
enabled  us  to  subject  the  quanta  of  radiant  energy 
to  a  control  capable  of  transforming  them  from 
theoretical  concepts  to  experimental  concepts. 
One,  however,  can  be  suggested,  drawn  from  the 
marvelous  properties  of  selenium.1 

1  Cf.  Fournier  d'Albe,  The  Future  of  Selenium  (Scientia,  1917, 
p.  165-191). 


142  PHILOSOPHY    AND    THE    NEW    PHYSICS 

When  one  of  the  conductors  in  an  electric  cir- 
cuit consists  of  selenium,  a  current  is  produced  in 
this  circuit,  as  soon  as  it  is  subjected  to  a  luminous 
flash.  The  conductivity  thus  produced  from  an 
instantaneous  exposure  of  the  selenium  to  light  is 
proportional  to  the  incident  energy.  This  property 
makes  it  possible  to  detect,  electrically,  flashes  that 
are  invisible  to  the  naked  eye.  By  applying,  for 
example,  an  electromotive  force  of  1  volt,  an  easily 
perceptible  current  of  10~12  ampere  could  be  ob- 
tained with  a  cell  of  selenium  of  100  sq.  cm.,  with 
a  short  flash  of  10~9  lux,  corresponding  to  a  star 
of  8th  or  9th  magnitude,  which  is  quite  invisible 
to  the  naked  eye.  With  a  selenium  cell  of  the 
same  surface  as  the  pupil  of  the  eye,  a  star  of 
the  6th  order,  which  is  the  extreme  limit  of  our 
vision,  could  be  detected  electrically  under  the 
same  conditions.  But,  since  we  are  able  to  measure 
currents  of  10~15  ampere,  the  sensitiveness  of 
selenium  obviously  surpasses  that  of  the  eye.  Now 
the  quantum  theory  permits  the  calculation  of  the 
size  and  number  of  the  grains  of  energy  absorbed  by 
a  given  surface,  subject  to  a  radiation  of  definite 
wave-length  and  intensity.  It  is  found  that  the 
human  eye  absorbs  360  quanta  per  second,  when 
it  receives  light  coming  from  the  visible  star  of 
least  luminosity.  These  quanta  are,  in  the  most 
favorable  case,  20  times  too  numerous  to  be  per- 
ceived as  distinct  flashes.  We  can  then  hope  to 
count  them  electrically,  aided  by  the  selenium,  if 
we  can  succeed  in  detecting  sufficiently  feeble  cur- 


PHYSICS    OF   THE    DISCONTINUOUS  143 

rents.  The  selenium  cell  would  thus  render  to  us 
the  same  service  as  the  zinc  sulfide  screen  of  Crookes' 
spinthariscope;  it  would  enable  us  to  place  the 
existence  of  the  quanta  on  an  experimental  basis. 

20.    THE  PHYSICS  OF  THE  DISCONTINUOUS. 

Modern  discoveries  lead  to  the  assumption  of  the 
discontinuity  of  matter,  of  electricity,  of  radiant 
energy,  and  of  exchanges  of  energy.  Henri  Poin- 
care  has  shown  the  consequences  that  result  there- 
from for  mathematical  physics  and  natural  philo- 
sophy. We  must  give  up  expressing  the  laws  of  the 
phenomena  in  the  form  of  differential  equations  in 
all  cases  in  which  the  large  number  of  elements 
which  come  into  play  does  not  suffice  to  wipe  out 
entirely  the  influence  of  the  individual  discontinui- 
ties. Contrary  to  the  ancient  adage  natura  non 
facit  saltus,  it  becomes  apparent  that  the  universe 
varies  by  sudden  jumps  and  not  be  imperceptible 
degrees.  A  physical  system  is  capable  of  only  a 
finite  number  of  distinct  states,  and  this  introduces 
discontinuity  into  the  distribution  even  of  probabil- 
ities. Since  between  two  different  and  immediately 
consecutive  states  the  world  remains  motionless, 
time  is  suspended  so  that  time  itself  is  discon- 
tinuous: there  is  an  atom  of  time. 

The  controversy  between  infinitists  and  finitists, 
idealists  and  empiricists,  cantorians  and  pragmat- 
ists,  to  follow  current  terminology,  is,  on  this  basis, 
settled  in  favor  of  the  latter.  The  world  does  not 
glide  smoothly  down  a  gentle  slope,  imperceptibly 


144  PHILOSOPHY   AND    THE    NEW    PHYSICS 

inclined,  of  the  course  of  events  according  to  Leibniz, 
but  it  descends  by  steps  of  events  as  conceived  by 
Evellin.1  In  the  external  reality  there  are  no  ag- 
gregates of  elements  having  the  attributes  of  a 
continuum  ,but  only  aggregates  that  can  be  counted, 
the  attributes  of  which  are  only  intelligible  for 
the  mind,  because  it  can  define  all  their  elements. 
Nature  following  mathematics  is  reduced  to  arithmetic. 
It  becomes  comprehensible,  for  if  our  imagination 
does  not  show  us  anything  except  in  the  form  of 
spatial  intuition,  which  is  that  of  a  physical  contin- 
uum, our  mind,  by  virtue  of  the  minimum  percepti- 
ble increment  of  excitation,  can  comprehend  only 
the  countable  and  the  discrete.  Just  as  continuity 
in  mathematics  appears  more  and  more  as  a  transi- 
tory tool,  the  utility  of  which  at  present  is  not  neg- 
ligible, but  which  must  be  regarded  as  a  means  of 
studying  the  countable  aggregates  that  constitute 
the  only  analytical  reality  that  is  accessible,  so  too 
physical  continuity,  which  lends  itself  well  to  appli- 
cations of  the  calculus  of  partial  derivatives,  will 
always  appear  legitimate,  as  a  first  approximation, 
for  the  order  of  magnitude  of  ensemble  effects  of 
systems  the  elements  of  which  are  finite  in  number 
but  sufficiently  numerous  to  wipe  out  the  individual 
discontinuities  by  virtue  of  perfect  mixing  and  the 
laws  of  chance.  Nevertheless  it  should  not  make  us 
forget  that  the  simple  elements  of  things  manifest  an 
essential  discontinuity,  which  must  reappear  in  the 
equations  that  -translate  their  individual  behavior 

*A  contemporary  French  philosopher.     (Tr.) 


PHYSICS    OF   THE    DISCONTINUOUS  145 

and  which  alone  can  account,  in  the  hypothesis  of 
the  absolute  determinism,  for  the  fluctuations  of  the 
ensemble  phenomena  to  which  they  give  rise. 

On  mathematical  physics  there  is  hereafter 
imposed  a  new  task,  namely,  to  establish  a  bond  :— 

Between  the  ensemble  phenomena  which  our 
observations  reveal,  and  the  elementary  phenomena 
of  which  they  are  a  statistical  resultant; 

Between  the  physical  quantities  directly  acces- 
sible to  our  measuring  instruments,  which  take 
in  at  once,  as  the  sum  or  average  of  the  individ- 
ual quantities,  so  many  elements  that  they  can  be 
practically  treated  as  continuous;  these  quantities 
being  in  themselves,  or  individually,  essentially 
discontinuous; 

Between  the  properties  of  the  discrete  grains 
(molecules,  atoms  and  electrons)  and  the  struc- 
tures they  form  by  aggregation. 

The  differential  and  integral  calculus,  used  to 
translate  analytically  the  idea  of  continuity,  is 
appropriate  for  the  study  of  the  systems  which 
alone  are  directly  perceptible,  and  which  are  com- 
posed of  a  very  great  number  of  elements.  The 
calculus  of  probabilities  is  appropriate  for  the  study 
of  the  relations  between  the  real  world  of  ele- 
ments of  discontinuous  structure  and  the  apparent 
world  of  continuous  phenomena;  between  the  indi- 
vidual laws,  which  govern  these  elements  taken 
separately,  and  the  laws  of  large  numbers,  which 
govern  the  mixed  appearances  to  which  their 
incessant  mixing  gives  rise. 

10 


146  PHILOSOPHY   AND    THE    NEW   PHYSICS 

By  correlation,  the  concept  of  explanation  be- 
comes transformed  in  natural  philosophy.  In 
former  days  a  physical  phenomenon  was  explained 
by  reducing  it  to  the  principles  of  classical  mechanics, 
by  giving  to  its  laws  the  form  impressed  by  Lagrange 
on  the  equations  of  dynamics.  To  explain  a  phen- 
omenon today  is  to  give  a  statistical  explanation, 
by  regarding  it  as  the  resultant  of  a  very  large 
number  of  underlying  phenomena  governed  by 
the  laws  of  chance.  Maxwell's  attempt  in  his 
Treatise  on  Electricity  and  Magnetism  is  an  example 
of  an  explanation  of  the  first  type.  The  statistical 
interpretation  of  Carnot's  principle,  of  the  expon- 
ential law  of  the  spontaneous  destruction  of  radio- 
active substances,  and  of  the  law  of  mass  action 
are  examples  of  the  second  type. 

Thus  not  only  do  the  most  fundamental  catego- 
ries of  our  mind,  those  of  space,  of  time,  and  of 
causality,  pass  through  an  evolution  with  the  pro- 
gress of  science,  but  the  same  holds  even  for  the 
concept  of  intelligibility.  To  explain  a  phenomenon 
is,  for  primitive  man,  to  interpret  it  anthropo- 
morphically  by  a  supernatural  agent  endowed  with 
psychological  life  in  his  own  image ;  for  a  scholastic 
it  is  to  explain  it  by  ultimate  causes;  for  Bacon  to 
explain  it  by  efficient  causes;  for  Maxwell  it  fc  to 
deduce  it  from  the  principles  of  mechanics;  for 
Gibbs  and  Boltzmann  it  is  to  account  for  it  by  the 
calculus  of  probabilities,  by  starting  from  a  system 
of  elements  subject  to  given  conditions.  Human 
reason  is  not  "u'ne  et  entidre  en  un  chacun"  as 


PHYSICS    OF    THE    DISCONTINUOUS  147 

Descartes  taught.  It  varies  with  the  abstract 
or  concrete  nature  of  our  thought,  and  in  proportion 
as,  on  contact  with  experimental  facts,  the  adapta- 
tion of  our  mind  to  nature  becomes  progressively 
realized. 


CHAPTER  VIII 
CONCLUSION 

21.    CONCLUSION. 

The  discoveries  of  modern  physics  have  led 
physicists  to  two  quite  distinct  conceptions  of  the 
universe. 

The  first  can  be  illustrated  by  the  suggestive 
name  of  the  dematerialization  of  matter.  It  con- 
sists in  reducing  matter  to  being  only  the  locus 
of  singular  points  of  torsion,  of  condensation,  or 
even  of  destruction  of  a  medium  endowed  with 
inertia  and  mechanical  properties,  the  dielectric 
ether  of  Faraday  and  Maxwell.  From  this  point 
of  view  an  electron  is  a  simple  cell  in  the  ether, 
behaving  like  a  projectile  moving  forward  in  a 
perfect  fluid  having  no  viscosity.  On  the  sides  of 
the  projectile  a  cushion  of  fluid  is  formed  and 
behind  it  a  zone  of  deep  eddies:  its  own  inertia  is 
increased  by  all  the  inertia  of  the  wave  system  thus 
created  which  follows  it.  At  start  a  part  of  the 
muzzle  energy  is  expended  in  overcoming  the  inertia 
of  the  fluid  displaced  at  the  same  time  as  the  inertia 
of  the  moving  body  itself;  but,  when  the  motion 
has  been  once  acquired,  it  perpetuates  itself  with- 
out resistance,  since  the  body  carries  its  wave 
system  with  it.  The  electron  has  no  inertia  of  its 
own,  but  it  can  not  be  displaced  without  entraining 

148 


CONCLUSION  149 

the"  surrounding  ether  coupled  to  its  lines  of  force, 
and  its  inertia  results  from  that  of  the  ether  thus 
disturbed  which  forms  its  electromagnetic  wave 
system.  Matter  resolves  itself  into  cells  in  the 
ether  and  the  ether  gains  in  substantiality  and  in 
reality  all  that  matter  loses. 

This  idea  results  from  Faraday's  work,  which 
has  brought  to  light  the  importance  of  the  medium 
that  surrounds  conductors  and  magnets  in  electric 
and  magnetic  phenomena.  The  attention  of  phy- 
sicists has  been  directed  to  the  study  of  electric 
and  magnetic  fields  in  which  energy  is  concentrated, 
matter  serving  only  as  a  support  of  these  fields. 
But  instead  of  conceiving  them  as  substantial 
realities  existing  in  an  independent  manner,  it  is 
claimed  that  they  are  explained  by  the  mechanical 
states  of  this  hypothetical  medium,  the  ether,  elec- 
tric energy  being  merely  the  potential  energy  of  its 
deformations  and  magnetic  energy  merely  the 
kinetic  energy  of  its  displacements.  The  ether 
becomes  the  active  medium  in  which  the  transfers 
and  the  transformations  of  energy  are  governed 
by  the  equations  of  the  electromagnetic  field  of 
Maxwell  and  Hertz,  and  thus  matter  is  gradually 
stripped  of  all  its  physical  contents  and  they  are 
referred  to  the  ether,  which  becomes  the  only  reality 
that  continues  to  exist. 

Going  still  further   Dr.   Gustave  Le  Bon1  has 

1  Dr.  G.  Le  Bon,  L' evolution  de  la  matiere.  On  the  relations 
and  the  differences  between  this  theory  and  that  of  Einstein  see 
L.  Rougier,  L'inertie  de  1'energie  (Revue  scientifique,  October 
13-20,  1917). 


150  PHILOSOPHY    AND    THE    NEW    PHYSICS 

developed  the  idea  of  the  evolution  of  matter. 
Let  us  imagine  that  the  electrons,  into  which  in  the 
end  the  molecular  structures  that  constitute  bodies 
are  resolved,  are  due  to  vortices  in  a  universal 
fluid  analogous  to  Lord  Kelvin's  gyrostatic  ether. 
Instead  of  regarding  these  vortices  as  indestructible 
in  conformity  with  the  hydrodynamic  equations  of 
Cauchy  and  Helmholtz,  let  us  imagine,  quite  gratui- 
tously, that  they  vanish  at  length  in  the  original 
fluid,  like  a  waterspout  in  the  ocean,  in  the  form 
of  liquid  waves,  owing  to  the  gradual  retardation 
of  their  velocity.  The  rotatory  energy  of  the 
electron  will  be  transformed  into  radiant  energy, 
which,  sweeping  through  all  space,  will  be  lost  at 
infinity.  Thus  matter  is  resolved  into  electrons, 
which  themselves  vanish  in  etherized  undulations, 
so  that  there  is  a  final  loss  of  matter  and  an  uncom- 
pensated  dissipation  of  energy.  For  the  universal 
principle  of  invariance  which  the  Ionic  natural 
philosophers  placed  at  the  basis  of  natural  philoso- 
phy and  which  assured  its  intelligibility,  namely, 
" Nothing  is  created,  nothing  is  lost"  one  must  now 
substitute  the  contrary  principle:  " Nothing  is 
created,  everything  is  lost/'  The  world  marches 
toward  a  final  bankruptcy,  and  the  ether,  of  which  it 
has  been  asserted  in  vain  that  it  is  the  matrix  of  the 
worlds,  is  revealed  as  being  their  final  tomb.  Thus 
Dr.  Gustave  Le  Bon  has  been,  in  sumptuous  prose, 
the  Zarathustra  announcing,  after  the  death  of  the 
gods,  the  twilight  of  their  creation. 

These  ideas  encounter  insurmountable  difficulties. 


CONCLUSION  151 

The  ether  is  revealed  as  endowed  with  contradictory 
mechanical  properties,  and  the  attempts  at  an 
explanation  of  electromagnetic  phenomena  start- 
ing from  it  have  all  suffered  shipwreck.  If  it 
exists  it  can  not  be  completely  entrained  by  matter, 
,as  Fizeau's  experiment  proves;  it  can  not  be  par- 
tially entrained  by  matter,  as  the  principle  of  action 
and  reaction  demonstrates;  that  it  can  not  be 
motionless,  is  implied  by  the  relativity  principle. 
Less  tangible  than  Proteus,  it  remains  only  to 
declare  it  defunct  without  estate. 

To  these  antinomies  the  theory  of  Dr.  Gustave 
Le  Bon  adds  new  difficulties.  The  hydrodyn  mic 
equations  of  Cauchy  and  Helmholtz  show  that 
vortices,  once  started  in  a  perfect,  homogeneous,  and 
incompressible  fluid,  are  eternal.  The  electronic 
theory  of  radiation  connects  its  appearance  with  the 
presence  of  electrons,  which  play  the  part  of  agents 
present  in  the  transformation  of  different  forms 
of  energy  into  radiation  and  permit  these  trans- 
formations, while  themselves  remaining,  like  cataliz- 
ing  agents,  unaltered.  Their  disappearance  would 
entail  therefore  that  of  radiation  itself,  in  which  they 
are  supposed  to  vanish.  Lastly,  if  the  principle 
of  invariance  of  the  Ionic  natural  philosophers  is 
abandoned,  the  very  possibility  of  science  is  put 
at  stake.  Science,  being  the  search  for  the  laws 
of  nature,  that  is  to  say,  the  invariants  of  all  events 
in  the  universe,  would  remain  valid,  to  a  first 
approximation,  only  for  systems  in  which  the  disin- 
tegration of  matter  and  the  radiation  of  energy  to 


152  PHILOSOPHY    AND    THE    NEW    PHYSICS 

infinity  are  practically  insignificant;  and  the  meta- 
physical problem  would  arise  of  understanding  how 
the  universe,  if  it  has  not  had  a  beginning,  has 
not  yet  finally  vanished,  milleniums  ago,  in  the 
"motionless  and  sleeping"  ether. 

Abandoning  the  ether,  we  are  led  to  an  en- 
tirely different  theory:  that  of  the  materialization 
of  energy.  Energy  emerges  from  the  phantom 
realm  of  imponderables  to  take  substance,  like  the 
shades  of  the  Elysian  fields  evoked  by  Ulysses  on 
the  Cimmerian  river.  It  appears  as  endowed  with 
inertia,  with  weight  and  structure  and  manifests 
itself  in  two  forms:  one  is  called,  by  virtue  of  long 
prescription,  matter;  the  other,  radiation. 

Matter  is  characterized  by  its  structure,  that 
is,  by  the  number  and  nature  of  the  electrons  and 
perhaps  the  positive  remainders  that  constitute 
it,  and  also  by  its  property  of  moving  with  veloci- 
ties, relatively  to  a  reference  system,  ranging  from 
0  to  V.  We  know  nothing  of  it,  as  stated  by  Ost- 
wald,  except  its  energetic  effects:  the  electric 
field  of  the  electron  at  rest,  the  magnetic  field 
of  the  electron  in  motion,  the  gravitational  field 
of  the  molecular  structures  formed,  by  electronic 
architecture,  the  kinetic  effects  produced  by  their 
vis  viva.  The  electron  is  revealed  as  a  grain  of  resi- 
nous (negative)  electricity,  so  that  matter  is  only 
a  form  of  energy,  enormously  accumulated  in 
a  narrowly  circumscribed  region  of  space.  It  does 
not,  on  that  account,  as  in  the  preceding  theory, 
lose  the  reality  and  the  substantial  characteristics 


CONCLUSION  153 

which  external  perception  and  common  sense  have 
agreed  until  now  to  attribute  to  it,  since  energy, 
which  is  its  essence,  is  endowed  with  mass,  weight, 
and  structure. 

Radiation  is  a  form  of  energy  which  no  longer 
appears  as  propagated  in  the  shape  of  continuous 
waves  by  a  hypothetical  medium,  but  as  expelled  in 
the  form  of  discrete  units  in  space  free  of  matter 
with  the  uniform  velocity  of  light.  It  also  is 
endowed  with  inertia,  weight,  and  structure.  Its 
possession  of  fundamental  properties  in  common 
with  matter  permits  the  explanation  of  its  action  on 
the  latter.  Luminous  radiation,  representing  a  cer- 
tain momentum,  can  be  strictly  assimilated  to  a 
material  projectile.  It  is  because  of  this  that,  by 
virtue  of  the  principle  of  action  and  reaction,  it 
exerts  a  repulsion  on  the  material  source  that  emits 
it  and  a  propulsion  on  a  material  obstacle  that  ab- 
sorbs it.  The  ancient  metaphysical  problem  of  the 
action  of  the  imponderable  on  the  ponderable,  of 
force  on  matter,  which  arose  in  its  most  modern  and 
most  urgent  form  in  connection  with  the  pressure  of 
radiation,  disappears  henceforth  as  a  pseudo- 
problem. 

BIBLIOGRAPHY 
1.  The  Relativity  Principle 

H.  A.  LORENTZ,  A.  EINSTEIN,  H.  MINKOWSKI,  Eine  Sammlung 
Abhandlungen,  Teubner,  1913. 

LAUE,  Das  Relativitatsprinzip,  Teubner,  1911. 

P.  LANGEVIN,  Le  temps,  1'espace  et  la  causalite  dans  la  Physique 
moderne  (Bulletin  de  la  Societ6  frangaise  de  Philosophie,  t.  XII, 
1912). 


154  PHILOSOPHY    AND    THE    NEW    PHYSICS 

2.  Electromagnetic  Dynamics 

H.  POINCARE,  La  theorie  de  Lorentz  et  le  principe  de  reaction 
(Archives  neerlandaises  des  Sciences  exactes  et  naturelles,  2e 
se"rie,  t.  V,  1900). 

H.  POINCARE,  Sur  la  dynamique  de  1' Electron  (Rendiconti  del 
Circolo  matematico  di  Palermo,  t.  XXI,  1905). 

P.  LANGEVIN,  Les  grains  d'electricite*  et  la  dynamique  electro- 
magnetique  (Les  ide"es  modefnes  sur  la  constitution  de  la  matiere, 
Paris,  1913). 

3.  The  Electronic  Theory  of  Matter 

P.  LANGEVIN  ET  M.  DE  BROGLIE,  Les  quantity's  e!6mentaires 
d'41ectricit4,  ions,  electrons,  corpuscules,  2  vol.,  Paris,  1905. 

Les  idees  modernes  sur  la  constitution  de  la  matiere  (Memoires 
de  la  Societe  franc,  aise  de  Physique,  Paris,  1913). 

N.  R.  CAMPBELL,  Modern  Electrical  Theory,  Cambridge,  1913. 

4.  The  Inertia  of  Energy 

A.  EINSTEIN,  Annalen  der  Physik,  vol.  XVIII,  1905. 
P.  LANGEVIN,  L'inertie  de  1'energie  et  ses  consequences  (Journal 
de  Physique,  juillet  1913). 

5.  The  Weight  of  Energy  and  the  Theory  of  Gravitation 

A.  EINSTEIN,  Annalen  der  Physik,  vol.  XXXV,  1911;  Ibid., 
vol.  XXXVII,  1912;  Physikalische  Zeitschrift,  vol.  XIV,  1913. 

A.  EINSTEIN  ET  GROSSMANN,  Bases  physiques  d'une  theorie 
de  la  gravitation  (Archives  des  Sciences  physiques  et  naturelles, 
t.  XXXVII,  1914). 

A.  EINSTEIN,  Die  formalen  Grundlagen  der  allgemeinen  Rela- 
tivitatstheorie  (Sitzungsberichte  der  koniglich  preussischen  Akade- 
mie  der  Wissenschaften,  vol.  XLI,  1914). 

A.  EINSTEIN,  Erklarung  der  Perihelbewegung  des  Merkur 
aus  der  allgemeinen  Relativitatstheorie  (Sitzungsberichte  der 
koniglich  preussischen  Akademie  der  Wissenschaften,  vol.  XLII, 
1915). 

H.  A.  LORENTZ,  La  gravitation  (Scientia,  1914). 

ED.  GUILLAUME,  Les  bases  de  la  Physique  moderne  (Archives 
des  Sciences  physiques  et  naturelles,  1916). 

L.  BLOCK,  Relativite  et  gravitation,  d'apres  16s  theories  recentes 
(Revue  generate  des  Sciences  pures  et  applique*es,  15  de"cembre 
1917). 


BIBLIOGRAPHY  155 

L.  BLOCH,  Sur  les  theories  de  la  gravitation  (Annales  de  Phy- 
sique, janvier-fevrier  1918). 

6.  The  Structure  of  Energy 

P.  LANGEVIN  ET  M.  DE  BROGLIE,  La  the"orie  du  rayonnement 
et  les  quanta,  Paris,  1912. 

H.  POINCARE,  Sur  la  theorie  des  quanta  (Journal  de  Physique, 
Janvier  1912). 

H.  POINCARE,  L'hypothese  des  quanta  (Revue  rose,  24  fevrier 
1912). 

P.  LANGEVIN,  La  physique  du  discontinu  (Les  progres  de  la 
physique  moleculaire,  Paris,  1914). 

M.  PLANCK,  Die  physikalische  Struktur  des  Phasenraumes 
(Annalen  der  Physik,  vol.  L,  1916). 

P.  S.  EPSTEIN,  Zur  Quantentheorie  (Annalen  der  Physik,  vol. 
LI,  1916). 

A.  EINSTEIN,  Zur  Quantentheorie  der  Strahlung  (Physikalische 
Zeitschrift,  vol.  XVIII,  1917). 

Other  Works  by  L.  Rougier : 

Les  Paralogismes  de  Rationalisme,  Paris,  1920.  La  philos- 
ophic ge*ometrique  de  Henri  Poincare,  Paris,  1920.  En  marge 
de  Curie  et  d'Einstein,  Paris,  1920.  Theories  formelles  et 
logique  deductive,  Paris,  1921. 


INDEX  OF  NAMES 


Abraham,  52,  54,  55,  56,  63, 
Arrhenius,  16 
Avogadro,  132 

Bacon,  146 
Bartoli,  17,  77 
Becquerel,  60 
Bernoulli!,  7 
Bloch,  154,  155 
Boltzmann,  9,  125,  146 
Le  Bon,  149,  150,  151 
Boscovich,  10,  11 
Brace,  31 
Brillouin,  xiii 
de  Broglie,  120 
Bucherer,  17,  56,  57,  63,  76 
Buisson,  xiii,  95 

Campbell,  70,  154 
Carnot,  126,  146 
Cauchy,  150,  151 
Christoffel,  98 
Clausius,  16 
Comte,  ix,  14 
Coulomb,  41,  53 
Cremieu,  48 

Crookes,  16,  54,  55,  58,  65, 
.    143 


76  Einstein,  x,  xii,  xiii,  xiv,  22,  26, 
27,  29,  70,  77,  93,  94,  97,  100, 
101,  103,  105,  106,  107,  109, 
132,  133,  134,  137,  138,  153, 
154,  155 

Enriques,  22 

Eotvos,  xiii,  18,  26,  84,  91,  96, 
100 

Epstein,  155 

Euclid,  20,  37,  100 

Euler,  99 

Evellin,  144 

Fabry,  xiii,  95 

Faraday,  16,  41,  43,  44,  45,  46, 

47,  49,  62,  63,  67,  70,   104, 

106,  148,  149 
Fizeau,  68,  151 
Fitz-Gerald,  31 
Foucault,  62 
Fournier  d'Albe,  141 
Fourier,  14 
Fraunhofer,  xiii,  95 
Fresnel,  62,  64,  68 
Freundlich,  96 


Descartes,  10,  100,  147 
Democritus,  7 
Du  Bois-Reymond,  ix 
Duhem,  x,  7,  106 
Dulong,  133,  134 

Edison,  58,  61,  65 


id.1 
W*      Galileo,  38,  39,  40,  62 

Gibbs,  146 
Goldstein,  60 
Grimaldi,  62 
Grossmann,  154 
Guillaume,  154 


157 


Hamilton,  40,  58,  126 
Hannequin,  7,  63 


158 


INDEX    OF   NAMES 


Helmholtz,  9,  106,  150,  151 
Hertz,  8,  9,  11,  20,  47,  48,  58, 

61,  65,  68,  120,  135,  139,  141, 

149 

van't  Hoff,  16 
Hupka,  56 
Huygens,  7,  62 

Janet,  5 
Jeans,  128 

Kant,  10,  11,  103 
Kaufmann,  17,  56,  57,  63,  76 
Kelvin,  9,  10,  70,  104,  106,  150 
Kirchhoff,  121 

Lagrange,  39,  40,  58,  146 
Langevin,  xiv,  29,  77,  91,  120, 

153 

Laue,  29,  153 
Lavoisier,  4,  90 
Lebedew,  17,  77 
Leibniz,  144 
Lenz,  48,  116 
Leonardo  da  Vinci,  62 
Leukippus,  7 
Levi-Civita,  98 
Lobatschewsky,  37 
Lodge,  70,  104,  106 
Lorentz,  29,  31,  32,  35,  36,  37, 

38,  39,  40,  55,  56,  57,  58,  60, 

61,  63,  72,  73,  74,  76,  79,  103, 

104,  105,  139,  153 

Mach,  27,  98 

Maupertuis,  23,  25 

Maxwell,  xiv,  9,  10,  11,  16,  17, 
20,  39,  40,  43,  47,  48,  49,  52, 
53,  58,  62,  63,  64,  67,  69,  70, 
74,  76,  77,  120,  125,  137,  146, 
148,  149 


Mayer,  4 

Meyerson,  7 

Michelson,  29,  31,  32,  38 

Mie,  96 

Millikan,  138 

Minkowski,  29,  35,  84,  100,  153 

Morley,  29,  31 

Mosotti,  41 

Nernst,  132,  133 
Neumann,  xiv 

Newton,  xiv,  17,  22,  25,  39,  58, 
70,  79,  86,  93,  98,  99,  102,  107 
Noble,  31 
Nordstrom,  96 

Onnes,  134 

Ostwald,  x,  3,  11,  12,  13,  14,  16, 
18,  19,  72,  110,  152 

Pasteur,  106 

Petit,  133,  134 

Planck,  xii,  124,  129,  130,  131, 

132,  133,  134,  137,  138,  139, 

155 
Poincare,  ix,  x,  73,  76,  79,  154, 

155 
Prout,  xiii,  92 

Rankine,  xi,  31 

Rayleigh,  31,  128,  129,  130 

Ricci,  98 

Rontgen,  117 

Rougier,  25,  38,  149 

Rowland,  16,  47,  48,  49,  76 

Salisbury,  63 
Spencer,  9 
Stallo,  7 
Stark,  136,  137 
Stefan,  123 


INDEX    OF   NAMES  159 


Tait,  10  Weber,  107 

Tisserand,  107  Wien,  58 

Thomson,  47,  67,  76,  137,  140  Wilson,  141 

Trouton,  31  Witte,  69 

Verne,  28  Zeeman,  61 


-°o  ON  THE 


MAR  251933 
SEP  161934 


. 


13 


.'141940 


REC'D  LD 

JAN  20  1957 


YB  09921 

-  ^ 


s*ntn> 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


